HIGH  SCHOOL  PHYSICS 


BY 

JOHN   O.   REED,   PH.D. 

DEAN   OF   THE    DEPARTMENT   OF   LITERATURE,    SCIENCE   AND   THE 

ARTS,    AND    HEAD    OF   THE    DEPARTMENT   OF   PHYSICS 

UNIVERSITY   OF   MICHIGAN 

AND 

WILLIAM  D.   HENDERSON,   PH.D. 

JUNIOR    PROFESSOR   OF  PHYSICS,    UNIVERSITY   OF    MICHIGAN 


LYONS    &    CARNAHAN 
CHICAGO  NEW  YORK 


COPYRIGHT, 
BY    LYONS    &    CARNAHAN 


THE'PLIMPTON'PRESS 
NORWOOD-MASS-U'S-A 


ex3. 


PREFACE 

THIS  text  is  offered  to  teachers  of  elementary  physics  with 
the  hope  that  it  will  not  only  prove  to  be  teachable  in  method, 
but  also  that  it  may  possess  that  " human  touch"  which  will 
make  it  interesting  to  read  as  well  as  profitable  to  study. 
The  chief  characteristics  of  the  book  are: 

(a)    CONTENT:   The    essentials    of    elementary  physics. 
(6)    LANGUAGE:    Simple     in     style     and     accurate     in 
statement. 

(c)  ILLUSTRATIONS:    Of    the    five    hundred    and    fifty 
illustrations  used  more  than  three  hundred  are  line  engravings, 
especially  prepared  to  serve  as  part  of  the  regular  recitation  work. 

(d)  EXERCISES:    The  exercises  and  problems  are  simple 
in  content  and  are  placed  in  the  text  in  immediate  connection 
with  the  topics  which  they  were  written  to  explain. 

(e)  SUPPLEMENT:    Herein    is    placed    a    large    amount 
of  supplementary  material,  as  for  example:   (a)    Presentation 
of  topics  of  special  interest  to  certain  localities  and  individual 
students,  (b)  discussion  of  modern  theories,  such  as  the  elec- 
tron theory  of  matter,  (c)  biographical  sketches,  (d)  tables  of 
physical  constants,   (e)  supplementary  problems.      This  sup- 
plementary material  is  classified  and  placed  in  order,  where  it 
may  be  made  use  of  as  occasion  and  opportunity  demand. 

The  authors  desire  to  thank  their  colleagues,  of  the 
University  of  Michigan,  Dr.  Karl  E.  Guthe,  Dean  of  the 
Graduate  Department,  Prof.  N.  H.  Williams,  and  Mr.  L.  D. 
Rich,  for  a  careful  and  critical  reading  of  the  manuscript. 

JOHN  0.  REED 

WILLIAM  D.  HENDERSON 

ANN  ARBOR,  May,  1913 


£94640 


CONTENTS 

INTRODUCTORY 

PAGE 

CHAPTER  I.    FUNDAMENTAL  PHYSICAL  CONCEPTS 1 

General  Principles 1 

Standards  of  Measurement 7 

MECHANICS 

CHAPTER  II.  FORCE  AND  MOTION 15 

Motion,  Velocity,  Acceleration 15 

Newton's  Laws  of  Motion 22 

Units  of  Force 26 

Composition  and  Resolution  of  Forces 28 

CHAPTER  III.  MECHANICS  OF  SOLIDS 36 

Centrifugal  Force  and  its  Applications 36 

Gravitation,  Gravity,  Center  of  Gravity,  Stability  ....  38 

The  Pendulum 44 

Work,  Power,  Energy 52 

Machines 57 

CHAPTER  IV.  MECHANICS  OF  FLUIDS 70 

Properties  of  Fluids 70 

Pressure  Due  to  Liquids 73 

Buoyancy  of  Liquids 79 

Density  and  Specific  Gravity 82 

Pressure  Due  to  Gases 88 

Applications  of  Air  Pressure 96 

CHAPTER  V.  MOLECULAR  MECHANICS 106 

Some  Special  Properties  of  Matter 106 

Surface  Tension  and  Capillary  Action 114 

Diffusion  and  Absorption 119 


vi  CONTENTS 

HEAT 

CHAPTER  VI.    HEAT 123 

Temperature 123 

Measurement  of  Heat 129 

Expansion 132 

Change  of  State 139 

Cold  by  Artificial  Means 150 

Transmission  of  Heat 152 

Relation  of  Heat  to  Work 165 

ELECTRICITY  AND  MAGNETISM 

CHAPTER  VII.     MAGNETISM  AND  ELECTROSTATICS 172 

Magnetism 172 

Static  Electricity 182 

CHAPTER  VIII.     CURRENT  ELECTRICITY 197 

The  Electric  Cell 197 

Kinds  of  Cells  .      .   • 203 

Chemical  Effects  of  a  Current 205 

Units  of  Electrical  Quantities 212 

Magnetic  Effects  of  a  Current 213 

Electrical  Measuring  Instruments 218 

Ohm's  Law  and  its  Applications 221 

Heating  Effect  of  a  Current 231 

Power  Expended  by  a  Current 237 

CHAPTER  IX.    ELECTROMAGNETIC  INDUCTION 240 

Induced  Electromotive  Force 240 

The  Dynamo  and  its  Use 245 

Electromagnetic  Appliances 256 

High  Potential  Phenomena 263 

SOUND 

CHAPTER  X.     SOUND 273 

Sound  and  Wave  Motion 273 

Transmission  of  Sound 278 

Loudness  and  Intensity  of  Sound 282 

Resonance  and  Interference 284 

Pitch  and  Music 291 

Vibration  of  Strings 297 

Vibration  of  Air  in  Pipes 299 

Organs  of  Voice  and  Hearing 302 


CONTENTS  vil 

LIGHT 

CHAPTER  XI.    LIGHT 309 

Nature  of  Light 309 

Intensity  of  Light 314 

Reflection    ..." 318 

Refraction 328 

Lenses 334 

Optical  Instruments 341 

Color  and  Dispersion 348 

SUPPLEMENT 

NOTES  AND  EXPLANATIONS 361 

TABLES  OF  PHYSICAL  CONSTANTS 393 

PORTRAITS  OF  EMINENT  PHYSICISTS 396 

ADDITIONAL  EXERCISES  AND  PROBLEMS 397 

INDEX.  405 


HIGH    SCHOOL    PHYSICS 

CHAPTER  I 
FUNDAMENTAL   PHYSICAL    CONCEPTS 

GENERAL  PRINCIPLES 

1.  Definition  of  Physics.     Science  is  commonly  denned  as 
classified  knowledge.     Botany  and  zoology,  which  deal  with 
living  things,  are  said  to  belong  to  the  biological  sciences; 
astronomy,  physics,  and  chemistry,  on  the  other  hand,  belong 
to  the  physical  sciences.     Physics  treats  of  the  related  phenom- 
ena of  matter  and  energy;   it  includes  the  subjects  of  mechanics, 
heat}  magnetism,  electricity,  sound,  and  light. 

2.  Matter.     Science  has  not  yet  definitely  determined  just 
what  matter  is,  and  for  this  reason  we  do  not  ordinarily  attempt 
to  define  it  in  any  specific  manner  other  than  to  say  that  it 
possesses  certain  characteristic  properties,  such  as  extension, 
indestructibility,  weight,  etc.     Matter,  however,  may  be  de- 
fined in  a  general  way  as  anything  which  occupies  space  and 
has  weight.     Thus  wood,  water,  and  air  are  forms  of  matter, 
for  it  may  be  shown  that  all  three  occupy  space  and  have 
weight.     Electricity,  heat,  and  light,  on  the  other  hand,  are 
not  generally  considered  to  be  forms  of  matter;   they  do  not, 
in  the  ordinary  sense  of  the  term,  possess  weight. 

3.  Energy.     Perhaps  no  two  words  occur  more  often  in 
physics  than  the  words  energy  and  force,  and  while  we  shall 
reserve  a  more  complete  discussion  of  these  subjects  until  a 
later  chapter,  yet  it  is  necessary  at  the  very  beginning  of  our 


2  HIGH  SCHOOL  PHYSICS 

study  to  define  in  a  general  way  these  most  important  terms. 
Energy  is  the  capacity  for  doing  work.  Whenever  anything  is 
capable  of  doing  work  in  any  form  whatsoever  we  say  that 
it  possesses  energy.  Thus  the  human  body  possesses  energy 
because  it  is  capable  of  doing  work.  Likewise  the  steam  in 
an  engine,  the  water  in  a  mill  dam,  the  coiled  spring  of  a  watch 
which  has  been  wound,  all  possess  energy.  It  should  be  noted 
that  energy  does  not  necessarily  imply  the  doing  of  work,  but 
the  capacity  to  do  work. 

4.  Force.     Whenever  we  push  or  pull  a  body  we  exert  force 
upon  it  and  the  body  tends  to  move.     In   every  act  of  life, 
therefore,   forces  manifest  themselves.     In  walking,  writing, 
rowing  a  boat,  or  pulling  a  sled  we  exert  force;    that  is,  we 
exert  pushes  or  pulls.     A  force  always  implies  a  push  or  a  pull, 
and  whenever  a  force  acts  upon  a  body  it  tends  to  set  it  in  motion. 

5.  The  Forces  of  Nature.     Nature  is  the  name  given  to  the 
world  which  we  see  around  us  —  the  sky,  the  hills,  the  rivers, 
the  sunshine.     We  speak  of  the  forces  generated  by  the  heat 
of  the  sun,  those  manifested  in  the  waterfall,  the  bursting  force 
of  frost,  etc.,  as  the  forces  of  nature.     We  see  these  forces 
operating  everywhere  about  us.     The  hills  are  washed  down, 
rocks  are    broken    into    tiny  fragments,   day  follows  night, 
summer  follows  winter.     Changes  due  to  the  forces  of  nature 
are  constantly  going  on,  yet  man  has  learned  by  experience 
that  these  changes  do  not  "just  happen";  they  take  place  in  a 
perfectly  definite  and  orderly  manner,  in  accordance  with  what 
are  called  the  laws  of  nature. 

6.  Phenomenon,   Theory,   Law.     A  natural  phenomenon  is 
anything  occurring  in  nature.     The  rising  of  smoke,  the  fall- 
ing of  rain,  the  sound  of  a  whistle,  the  flying  of  a  kite  are  all 
examples  of  natural  phenomena. 

A  theory  is  a  reason  put  forth  to  explain  phenomena.  Thus, 
in  order  to  explain  the  motions  of  the  heavenly  bodies,  we 
assume  that  every  particle  of  matter  in  the  universe  attracts 
every  other  particle.  This  is  called  the  theory  of  gravitation. 


FUNDAMENTAL   PHYSICAL   CONCEPTS  3 

A  law  is  a  definite  statement  regarding  physical  phenomena, 
and  is  capable  of  being  verified  by  experiment. 

An  experiment  is  a  question  put  to  nature.  All  experimenta- 
tion is  based  on  the  assumption  of  the  constancy  of  nature; 
we  assume  that  under  the  same  conditions  nature  always  acts 
in  the  same  manner. 

7.  Extension.     Extension  is  that  property  of  matter  by  vir- 
tue of  which  it  occupies  space.     A  fountain  pen,  for  example, 
is  a  portion  of  matter.      It  is  made  of  two 
substances,  the  metal  of  the  pen  and  the  rub- 
ber of  the  holder.     It  occupies  space;  it,  there- 
fore, possesses  the  property  of  extension.     Air 

is  matter.      That  it  occupies  space  may  be 
shown  by  a  very  simple  experiment.     If  we 
thrust  a  tumbler  mouth  downward  into  water, 
Fig.  1,  we  observe  that  the  water  does  not  fill 
it  because  the  air  within  occupies  a  part  of  the  space.     The 
water  rises  in  the  tumbler  a  little  way  because  the  air  is  some- 
what compressed.     It  is  evident  that  the  air  occupies  space; 
hence  we  say  that  air  possesses  the  property  of  extension. 

8.  Matter    Indestructible.     Matter    cannot    be    destroyed. 
If  a  piece  of  chalk,  for  example,  be  ground  to  the  finest  powder 
and  thrown  to  the  winds,  we  have  not  destroyed  the  chalk,  but 
have  simply  changed  its  form.     Or  again,  if  we  throw  a  piece 
of  paper  into  the  fire  and  it  is  consumed,  we  have  not  by  this 
act  destroyed  a  single  particle  of  matter.     We  have  changed 
both  the  form  and  the  identity  of  the  paper,  but  we  have  -not 
destroyed  the  matter  of  which  it  is  composed. 

9.  The  Structure  of  Matter.     According  to  present  theories, 
matter  is  composed  of  small  particles  which  are  in  constant 
motion.    These  particles,  which  are  so  small  as  to  be  invisible 
under  the  most  powerful  microscope,  do  not  rest  one  upon 
another,  as  do  bricks  in  a  wall,  but  are  constantly  striking 
against    each    other,    bounding   back   and   forth   with   great 
rapidity.     In  view  of  this  theory,  the  question  at  once  arises, 


4  HIGH  SCHOOL  PHYSICS 

How  does  matter  retain  its  form?  If  the  particles  of  a  piece 
of  chalk  are  in  constant  motion,  how  does  the  chalk  retain 
its  shape?  The  ancients  supposed  that  the  particles  of  which 
matter  is  composed  were  held  together  by  hooks  or  claws; 
we  of  to-day  assume  that  they  are  held  together  by  invisible 
forces  which  allow  considerable  freedom  of  motion,  yet  which 
restrain  the  particles  within  the  form  of  the  body. 

10.  Molecules,    Atoms,    and   Electrons.      The   particles   of 
which  we  have  just  been  speaking  are  called  molecules.     A 
molecule  is  the  smallest  particle  of  a  substance  that  can  exist 
by  itself  and  retain  its  identity.     Thus,  a  molecule  of  water 
is  the  smallest  particle  that  can  exist  as  water.     A  glass  of 
water  is  composed  of  many  drops;   each  drop  may  be  divided 
into  smaller  and  smaller  parts  until,  it  may  be  conceived,  we 
come  to  the  smallest  particle  that  can  exist  as  water.    This  is 
the  molecule.      If  we  carry  the  division  further,  as  may  be 
done  by  chemical  means,  we  no  longer  have  water,  but  two 
gases,  hydrogen  and  oxygen.     Molecules,  then,  are  made  up  of 
still  smaller  particles  called  atoms.     Thus,  a  molecule  of  water 
contains  two  atoms  of  hydrogen  and  one  of  oxygen. 

There  are  many  reasons  which  lead  modern  scientists  to 
believe  that  atoms,  in  turn,  may  be  made  up  of  still  smaller 
electrically  charged  particles  called  corpuscles  or  electrons. 
(Supplement,  article  595.) 

11.  Chemical  Symbols.     The  chemical  symbol  for  a  mole- 
cule of  water  is  H2O.     This  means  that  a  molecule  of  water 
contains  two  atoms  of  hydrogen  (H)  and  one  atom  of  oxy- 
gen (0).     A  molecule  of  common  table  salt,  sodium  chloride,  is 
written  NaCl;   that  is,  the  molecule  is  made  up  of  one  atom 
of  sodium   (Na)   and  one  atom  of  chlorine   (Cl).     In  a  like 
manner  sulphuric  acid  is  written  H2S04,  where  S  stands  for 
sulphur. 

EXERCISE.  1.  (a)  How  many  atoms  of  hydrogen  are  contained  in  a 
molecule  of  sulphuric  acid?  (b)  How  many  atoms  of  sulphur?  (c)  Of 
oxygen?  (d)  How  many  atoms  in  the  molecule? 


FUNDAMENTAL   PHYSICAL  CONCEPTS  5 

12.  States  of  Matter.     Matter  is  commonly  thought  of  as 
occurring  in  three  states  —  solid,  liquid,  and  gaseous,  as  illus- 
trated by  earth,  water,  and  air.     A  more  specific  classification, 
however,  would  assign  matter  to  two  general  conditions,  solid 
and  fluid.     A  solid  is  a  substance  that  retains  both  its  shape 
and  volume.     A  fluid  is  a  substance  that  will  flow.     Fluids  are 
divided  into  liquids  and  gases. 

13.  Distinction  between   Solids  and  Fluids.     In  everyday 
experience  we  have  no   difficulty  in  distinguishing  between 
solids  and  fluids.     We  do  not  hesitate  to  classify  the  pen  with 
which  we  write  as  a  solid  and  the  ink  as  a  fluid.     Nevertheless, 
in  a  great  many  cases  no  sharply  defined  dividing  line  can  be 
drawn  between  solids  and  fluids.     Indeed  there  is  a  contin- 
uous gradation  from  the  most  rigid  solids  to  the  rarest  gases. 
Steel  is  a  rigid  solid;   syrup  is  a  viscous  fluid.     Pitch  has  the 
properties  of  both  a  solid  and  a  fluid.     If   struck  a  sharp 
blow  with  a  hammer,  a  lump  of  pitch  will  break  like  glass;  if 
left  to  itself,  however,  it  will  flatten  out  of  its  own  weight 
and  will  flow. 

14.  Physical    and    Chemical    Changes.     Matter    may    be 
changed  in  two  ways,  physically  and  chemically.     A  physical 
change  is  one  which  does  not  alter  the  identity  of  the  substance. 
The  tearing  of  a  piece  of  paper  is  a  physical  change.     The  form 
of  the  paper  is  altered  by  the  tearing,  but  not  the  substance; 
each  piece  is  still  paper.     A  chemical  change  is  one  which  alters 
the  identity  of  the  substance.     The  burning  of  a  piece  of  paper, 
for  example,  is  a  chemical  change.     In  combustion  (burning) 
the  oxygen  (0)  of  the  air  unites  with  the  carbon  (C)  of  the 
paper,  forming  a  gas  called  carbon  dioxide  (C02) .     The  chemical 
reaction  is  represented  thus,  C  +  2O  =  C02. 

Sometimes  changes  occur  which  are  both  physical  and  chem- 
ical, as  illustrated  in  the  chewing  of  a  piece  of  bread.  The 
crushing  of  the  bread  with  the  teeth  is  a  physical  change;  the 
reaction  of  the  saliva  with  the  starch  of  the  bread,  changing  it 
to  sugar,  is  a  chemical  change. 


6  HIGH  SCHOOL  PHYSICS 

EXERCISE.  2.  (a)  What  change  is  involved  in  the  breaking  of  a  piece 
of  chalk?  (b)  In  the  burning  of  a  lump  of  coal?  (c)  In  the  melting  of  a 
piece  of  ice?  (d)  In  the  cooking  of  food?  (e)  In  the  dissolving  of  a  metal 
in  acid? 

15.  Mass.    The  mass  of  a  body  is  the  measure  of  the  quan- 
tity of  matter  it  contains.     This  is  simply  another  way  of  say- 
ing that  the  mass  of  a  body  is  the  measure  of  its  inertia,  that 
is,  its  resistance  to  change  in  its  condition  of  rest  or  motion. 
Thus,  if  two  bodies  of  the  same  size,  a  brick  and  a  block  of  wood, 
be  acted  upon  by  the  same  force,  it  will  be  found  that  the 
brick  offers  the  greater  resistance  to  being  set  in  motion;  that 
is,  it  possesses  the  greater  inertia,  and  hence  the  greater  mass. 

16.  The  Force  of  Gravity.     Daily  experience  teaches  us  that 
all  bodies  tend  to  fall  to  the  earth.     A  piece  of  chalk  held  in 
the  fingers  is  at  rest;  if  released  it  at  once  falls  to  the  floor.     Its 
condition  of  motion  is  changed.     Now  when  the  motion  of  a 
body  is  changed,  we  say  that  a  force  has  acted  upon  it.     The 
force  by  which  bodies  are  attracted  to  the  earth  is  called  the  force 
of  gravity.     The  apple  falls  from  the  tree  to  the  earth  because 
of  the  force  of  gravity;  rain  falls  from  the  clouds,  rivers  run  to 
the  sea,  bodies  everywhere  tend  to  fall  because  of  the  constant 
pull  exerted  by  the  force  of  gravity. 

17.  Weight.     The  weight  of  a  body  is  the  force  by  which  it  is 
attracted  to  the  earth;  weight  may  therefore  be  defined  as  the 
measure  of  gravity.     The  weight  of  a  body  depends  upon  two 
factors,  (a)  the  quantity  of  matter  which  it  contains  (its  mass) 
and  (b)  its  position  with  respect  to  the  earth.     Thus,  for  ex- 
ample, for  a  given  place  on  the  earth's  surface,  a  whole  brick 
weighs  more  than  a  half  brick,  because  the  first  has  more  mass 
than  the  second.     Also,  a  brick  at  the  surface  of  the  earth 
weighs  more  than  if  taken  some  distance  above  the  surface, 
because  the  force  of  gravity  is  greater  at  the  surface  than 
above  it. 

18.  Different  Uses  of  the  Term  Weight.     In  the  study  of 
mechanics  the  term  weight  occurs  many  times,  and  is  some- 


FUNDAMENTAL  PHYSICAL  CONCEPTS  7 

times  employed  in  three  different  senses,  as  follows:  (a)  The 
term  weight  is  used  when  referring  to  an  object,  as,  for  example, 
we  may  say,  "  Put  the  weight  on  the  scale  pan,"  meaning, 
thereby,  a  definite  piece  of  metal;  (b)  it  is  also  employed  to 
designate  a  force  equivalent  to  the  attraction  of  gravity,  as 
defined  in  the  preceding  topic;  and  (c)  the  word  weight  is 
frequently  used  as  synonymous  with  mass.  This  last  use  of 
the  term  is  confusing  and  misleading. 

19.  Distinction  between  Mass  and  Weight.     It  is  manifestly 
very  important  that  a  careful  distinction  be  made  between  the 
mass  of  a  body  and  its  weight.     Mass  refers  to  the  quantity  of 
matter  in  the  body;  weight,  to  the  force  with  which  the  earth 
attracts  the  body.     If  an  object  be  moved  from  one  place  to 
another,  its  mass  is  not  affected  thereby;    its  weight,  on  the 
other  hand,  may  be  changed,  since  the  weight  of  a  body  is  deter- 
mined by  the  force  of  gravity  acting  upon  it,  and  the  force  of 
gravity  for  a  given  mass  differs  slightly  for  different  points  upon 
the  earth's  surface. 

FUNDAMENTAL  UNITS  OF  MEASUREMENT 

20.  Fundamental  Units.     Since  the  study  of  physics  includes 
not  only  the  observation  and  classification  of  physical  phenom- 
ena, but  also  the  measurement  of  these  phenomena,  it  is  essen- 
tial that  we  have  at  the  very  outset  a  clear  understanding  of 
the  units  employed.     The  fundamental  units  for  all  physical 
measurements  are  those  of  length,  mass,  and  time. 

The  legal  standards  of  length  and  mass  in  the  United  States 
are  those  of  the  metric  system,  legalized  by  Act  of  Congress  in 
1866.  The  standard  of  length  is  the  meter;  the  standard  of 
mass  is  the  kilogram;  the  standard  of  time,  the  second. 

21.  The   Metric  Standards.     The  metric  system  was  first 
introduced  by  the  French  about  the  year  1793,  and  has  since 
been  adopted,  in  whole  or  in  part,  by  most  of  the  civilized 
countries  of  the  world.     The  meter  was  originally  intended  to 
be  equivalent  to  one  ten-millionth  of  an  earth  quadrant,  that 


8  HIGH   SCHOOL  PHYSICS 

is,  one-fourth  of  a  great  circle  of  the  earth;  and  the  kilogram 
was  intended  to  be  equivalent  to  the  mass  of  one  liter  of  pure 
water.  As  it  was  found  impossible,  however,  to  determine 
exactly  these  quantities,  there  were  arbitrarily  chosen  as  stand- 
ards a  meter  and  kilogram  which  are  only  approximately 
equal  to  the  theoretical  values  determined  upon  by  the  origi- 
nators of  the  system. 

The  meter  and  kilogram  which  were  finally  chosen  as  stand- 
ards, and  which  were  made  of  platinum,  are  kept  in  the  Palace 
of  the  Archives  at  Paris,  and  are  known  as  the  "  Standards  of 
the  Archives." 

22.  The  International  Metric  Standards.  In  1872  an  Inter- 
national Conference  of  Weights  and  Measures  was  called  to 
meet  at  Paris.  The  object  of  this  conference  was  to  consider 
the  question  of  International  Standards.  Thirty  countries 
responded,  the  United  States  being  among  the  number.  At 
this  meeting  three  things  were  accomplished:  (a)  An  Interna- 
tional Bureau  of  Weights  and  Measures  was  organized;  (b)  an 
International  Laboratory,  located  near  Paris,  was  established; 
and  (c)  the  construction  of  a  number  of  prototype  standards, 
similar  to  the  Standards  of  the  Archives,  was  authorized.  As 
a  result  of  this  conference  a  number  of  standard  meters  and 
kilograms  were  constructed  of  an  alloy  of  90  per  cent  platinum 
and  10  per  cent  iridium,  each  being  as  nearly  as  possible  an 
exact  duplicate  of  the  Standards  of  the  Archives.  That  meter 
and  that  kilogram  which  most  closely  corresponded  to  the 
meter  and  kilogram  of  the  Archives  were  chosen  as  the  Inter- 
national Standards,  and  were  deposited  in  the  International 
Laboratory,  where  they  are  now  kept  for  reference.  (Supple- 
ment, 534.)  Civilized  countries  have  entered  into  an  agree- 
ment whereby  this  International  Laboratory  is  considered 
neutral  ground,  thus  avoiding,  in  case  of  war,  any  danger  of 
injury  to  or  destruction  of  the  International  Standards.  The 
remaining  standards  were  disposed  of  by  lot  to  the  various 
countries  represented,  the  United  States  drawing  two  meters 


FUNDAMENTAL   PHYSICAL   CONCEPTS 


9 


FIG.  2.  —  Section  of  U.  S.  Standard  Meter 


FIG.  3.  —  U.  S.  Standard  Kilogram 


10  HIGH   SCHOOL   PHYSICS 

and  two  kilograms — meters  Nos.  21  and  27  and  kilograms  Nos. 
4  and  20.  As  has  already  been  stated,  these  standards  were 
brought  to  this  country  and  are  now  kept  in  the  Bureau  of 
Standards  at  Washington. 

A  very  good  idea  of  the  general  appearance  of  the  U.  S.  stand- 
ard meter  and  kilogram  may  be  obtained  from  Figs.  2  and  3, 
which  are  copies  of  actual  photographs.  Fig.  2  shows  a 
section  of  the  U.  S.  prototype  meter  No.  27,  and  Fig.  3  kilo- 
gram No.  20.  The  standard  kilogram  is  cylindrical  in  shape 
and  rests  upon  a  circular  base,  both  being  enclosed  under  two 
glass  bell  jars,  as  shown. 

23.  Two  Systems  of  Measurement.  In  some  countries, 
France  and  Germany  for  instance,  the  metric  system  is  used 
both  for  scientific  and  commercial  purposes.  In  the  United 
States  and  Great  Britain,  however,  two  systems  of  units  of 
length  and  mass  are  in  common  use,  the  metric  and  the  Eng- 
lish. The  metric  unit  of  length  is  the  meter;  the  English 
unit,  the  yard.  The  metric  unit  of  mass  is  the  kilogram;  the 
English  unit,  the  pound. 

A  distinction,  however,  must  be  made  between  the  English 
units  of  the  United  States  and  those  of  Great  Britain.  Our 
English  units,  the  inch,  the  foot,  the  yard,  the  pound,  etc., 
come  historically  from  those  of  England,  but  in  actual  prac- 
tice today  they  are  derived  from  our  national  metric  standards 
at  Washington.  For  example,  the  U.  S.  inch  as  defined  by 
Act  of  Congress  is  as  follows: 

1  inch  (U.  S.)  =  39137  of  1  meter. 

In  Great  Britain,  on  the  other  hand,  the  inch  is  defined  as 
~Q  of  a  standard  British  yard.  The  standard  British  yard  and 
pound,  together  with  the  metric  standards  of  that  country, 
are  kept  at  the  office  of  the  Exchequer  in  London. 

The  U.  S.  inch  is  slightly  longer  than  the  British  inch,  as 
shown  by  the  following: 

1  meter  =  39.37  U.  S.  inches  =  39.37079  British  inches. 


FUNDAMENTAL   PHYSICAL   CONCEPTS 


11 


24.  Units  of  Length.  The  metric  unit  of  length  is  the  meter, 
which  is  the  distance  between  two  marks  on  a  platinum-irid- 
ium  bar  kept  at  the  Bureau  of  Standards  at  Washington. 


CENTIMETER 

0          1 

I      , 


INCH 


LI  LI 


FIG.  4 

The  divisions  and  multiples  of  the  meter  are  given  in  the  fol- 
lowing tables.  The  relation  of  English  equivalents  is  shown 
in  Fig.  4.  For  fractions  of  the  meter  we  use  the  Latin  prefixes 
deci,  centi,  milli ;  for  multiples,  the  Greek  prefixes  deka,  hekto, 
kilo. 

Fractions  Multiples 

TV  meter  (m)  =  1  decimeter  (dm)         10  meters  =  1  dekameter  (dkm) 
yijtf  meter          =  1  centimeter  (cm)      100  meters  =  1  hektometer  (hkm) 
TFJJO  meter          =  1  millimeter  (mm)  1000  meters  =  1  kilometer  (km) 

25.  Units  of  Volume.  The  unit  of  volume  is  the  liter  (1). 
A  liter  is  the  volume  of  one  kilogram  of  air-free  distilled  water 
at  4°  C.  (Supplement,  535.)  Since  a  kilogram  of  pure  water, 
under  the  conditions  named,  has  a  volume  of  practically  one 
cubic  decimeter,  a  liter,  therefore,  may  be  considered  as  equiv- 
alent to  1000  cubic  centimeters;  that  is, 

1  liter  =  1000  cc.  =  1.0576  qts.  (liquid  measure). 

EXERCISES.  3.  Determine  the  length  and  width  of  the  laboratory 
table  in  (a)  metric  units;  (b)  English  units. 

4.  Draw  on  paper  (a)  a  square  centimeter;   (b)  square  inch;    (c)  square 
decimeter. 

5.  Give  the  equivalents  of  the  following  abbreviations:  m.,  cm.,  mm., 
km.,  in.,  ft.,  sq.  cm.,  cu.  cm. 

6.  Pour  a  quart  of  water  into  a  liter  measure  and  observe  how  nearly 
a  liter  equals  a  quart  in  volume. 


12 


HIGH   SCHOOL  PHYSICS 


7.   Find  the  volume  of  a  piece  of  metal  or  stone  by  means  of  a  graduate, 
as  shown  in  Fig.  5. 


26. 


Units  of  Mass.  We  have  already  defined  mass  as  the 
quantity  of  matter  contained  in  a  body.  It 
is  usually  measured  by  counterbalancing  the 
body  against  some  standard.  The  unit  of 
mass  in  the  metric  system  is  the  kilogram. 
A  kilogram  is  a  mass  equivalent  to  the  na- 
tional standard  kilogram. 

For  all  practical  purposes  the  gram  may 
be  considered  as  equivalent  to  the  mass  of  a 
cubic  centimeter  of  distilled  water  at  4°  C. 
It  must  be  remembered,  however,  that  this 
is  only  approximately  true,  a  gram  being, 
by  exact  definition,  10100  of  a  standard  mass 
known  as  the  standard  kilogram. 
The  divisions  of  the  kilogram  and  gram,  together  with  equiv- 
alents in  the  English  system,  are  as  follows: 

1  gram  =  ytfW  kilogram  (k)  1  gram  =  15.432  grains;  that  is, 

iV  gram  =  1  decigram  1  grain  =  15.132  gram 

T$TT  gram  =  1  centigram  1  kilogram  =  2.2046  pounds  (Av.) 
TnjW  gram  =  1  milligram  (mg) 

27.  The  Balance.     In  accurate  determinations  of  mass  we 
ordinarily  use  some  form  of  the  balance.     In  Fig.  6  there  is 
shown  one  type  of  the  analytic  balance,  and  in  Fig.  7  a  set  of 
standard  weights,  ranging  in  value  from  100  grams  to  1  gram. 
To  determine  the  mass  of  a  body  by  means  of  a  balance  we 
proceed  somewhat  as  follows:    The  given  body  is  placed  on 
one  of  the  scale  pans  of  the  balance  and  standard  weights  are 
added  to  the  other  pan  until  the  balance  is  in  equilibrium. 
The  mass  of  the  body  is  equal  to  the  mass  of  the  weights  required 
to  counterbalance  it. 

28.  Unit  of  Time.     The  unit  of  time  is  the  second.     A  sec- 
ond is  -g^iinr  of  a  mean  solar  day.     A  solar  day  is  measured 
from  sun  to  sun;  that  is,  from  the  time  the  sun  is  directly 


FUNDAMENTAL   PHYSICAL   CONCEPTS 


13 


overhead  until  it  is  in  the  same  position  again  on  the  follow- 
ing day.  Solar  days,  however,  vary  in  length  throughout  the 
year;  it  is  necessary,  therefore,  to  define  the  second  in  terms 


FIG.  6.  —  Analytical  Balance 


FIG.  7.  —  Set  of  Standard  Gram  Weights 

of  the  mean  solar  day.     A  mean  solar  day  is  the  average  length 
of  all  the  solar  days  taken  throughout  the  year. 


14  HIGH   SCHOOL  PHYSICS 

The  time  recorded  by  clocks  and  watches  is  expressed  in  mean 
solar  time. 

29.  F.P.S.  and  C.G.S.  Systems  of  Measurement.  When  in 
the  English  system  we  use  the  foot  as  the  unit  of  length,  the 
pound  as  the  unit  of  mass,  and  the  second  as  the  unit  of  time, 
we  speak  of  the  system  of  units  thus  employed  as  the  F.P.S. , 
or  foot-pound-second,  system.  Likewise,  when  in  the  metric 
system  we  use  the  centimeter  as  the  unit  of  length,  the  gram 
as  the  unit  of  mass,  and  the  second  as  the  unit  of  time,  we 
speak  of  it  as  the  C.G.S.  system  of  measurement. 


MECHANICS 

CHAPTER  II 
FORCE   AND    MOTION 

MOTION,  VELOCITY,  ACCELERATION 

30.  Mechanics.     The  term  mechanics,   as  originally  used, 
referred  to  the  study  of  machines.     It  has,  however,   come 
to  have  a  much  wider  meaning,  referring  in  a  general  way  to 
the  effect  of  forces  on  bodies.     The  force  exerted  by  a  loco- 
motive, that  exerted  in  the  batting  of  a  ball,  the  flying  of  a  kite, 
the  sailing  of  a  boat,  are  all  illustrations  of  the  principles  of 
mechanics. 

31.  Force.    When  we  push  or  pull  a  body  we  exert  force 
upon  it,  and  the  body  tends  to  move.     Force  is  that  which 
produces  or  tends  to  produce  motion.     Force  always  produces 
or  tends  to  produce  motion.     A  book  lying  on  a  table  exerts 
a   force   upon  the   table.     In   this   case    no   motion   is   pro- 
duced;  the  force  tends  to  produce  motion.     A  horse  pulling  a 
cart  exerts  force  upon  the  cart,  producing  motion.     The  rela- 
tion between  force  and  motion  is  very  well  illustrated  in  the 
playing  of  a  game  of  ball.     The  pitcher  exerts  force  upon  the 
ball,  producing  motion;   the  batter  exerts  force  upon  the  ball, 
changing  its  motion;  the  catcher  exerts  force  in  destroying  its 
motion. 

32.  Rest  and  Motion  Relative  Terms.     When  a  body  changes 
its  position  with  reference  to  a  fixed  point,  it  is  said  to  be  in 
motion.     Rest  and  motion  are  purely  relative  terms;  that  is  to 
say,  a  body  may  be  at  rest  with  reference  to  one  object,  and 
in  motion  with  reference  to  another.     For  example,  a  person 


16  HIGH   SCHOOL   PHYSICS 

sitting  quietly  in  a  moving  car  is  at  rest  with  respect  to  his 
seat,  but  is  in  motion  with  respect  to  objects  outside. 

EXERCISES.  1.  (a)  If  the  hand  be  clinched  and  moved  about,  are  the 
fingers  at  rest  or  in  motion  with  reference  to  each  other?  (b)  Are  they  at 
rest  or  in  motion  with  reference  to  the  body? 

2.  Consider  the  wheel  of  a  carriage  in  motion,     (a)  Are  the  spokes  at 
rest  or  in  motion  with  respect  to  each  other?     (b)  Are  they  at  rest  or  in 
motion  with  respect  to  the  earth? 

3.  Give  another  example  of  a  body  that  is  at  rest  in  its  relation  to  one 
object  and  in  motion  in  relation  to  another. 

33.  Kinds  of  Motion.     Motion  may  be  classified  with  refer- 
ence to  direction  as  (a)  rectilinear  or  straight-line  motion,  and 

(b)  curvilinear  or  curved-line  motion.     Motion  may  also  be 
classified  with  reference  to  rate  as  (a)  uniform  motion,  and  (b) 
varied  motion.     When  a  body  travels  over  equal  spaces  in  equal 
intervals  of  time,  its  motion  is  uniform;   when  it  travels  over 
unequal  spaces  in  equal  intervals  of  time,  its  motion  is  varied. 
There  is  probably  no  such  thing  in  the  universe  as  an  example 
of  absolutely  uniform  motion,  since  all  bodies  in  moving  change 
in  some  degree  their  rate.     We  can,  however,  imagine  such  a 
thing  as  uniform  motion,  or  we  may  find  examples  of  motion 
which  are  approximately  uniform. 

EXERCISE.  4.  Classify,  with  reference  to  direction  and  rate,  the  fol- 
lowing motions:  (a)  The  piston  of  a  steam  engine;  (b)  the  hands  of  a  clock; 

(c)  the  flywheel  of  an  engine;   (d)  the  rotation  of  the  earth  on  its  axis. 

34.  Velocity.     Velocity  is  the  rate  of  motion  per  unit  of  time. 
It  is  usually  expressed  in  miles  per  hour,  feet  per  second,  or 
centimeters  per  second.     The  term  velocity,  when  used  in  a 
strictly  scientific  sense,  refers  to  the  rate  of  motion  of  a  body 
in  a  definite  direction;  speed,  on  the  other  hand,  refers  to  the 
rate  of  motion  without  reference  to  direction.     Thus,  when  we 
speak  of  the  speed  of  a  race  horse,  we  refer  to  its  rate  of 
motion  only,  without  reference  to  any  particular  direction. 

The  mean  or  average  velocity  of  a  body  is  found  by  dividing 
the  space  passed  over  by  the  time. 


FORCE  AND   MOTION  17 

EXERCISE.  6.  If  a  train  run  120  miles  in  4  hours,  what  will  be  its  aver- 
age velocity  in  (a)  miles  per  hour?  (b)  feet  per  hour?  (c)  feet  per  second? 

35.  Acceleration.     When  the  velocity  of  a  body  increases 
or  decreases,  its  motion  is  said  to  be  accelerated.     Accelera- 
tion is  the  change  of  velocity  per  unit  of  time.     If  there  is  an 
increase  of  velocity  per  unit  of  time,  the  acceleration  is  called 
positive;    if  a  decrease,  negative.     The  symbol  for  positive 
acceleration  is  +  a;   for  negative,  —  a.      Velocity  is  expressed 
in  units  per  second;   acceleration,  in  units  per  second  per  sec- 
ond.   Thus,  when  we  say  that  a  body  has  an  acceleration  of 
10  centimeters  per  second  per  second,  we  mean  that  its  velocity 
has  increased  or  decreased  by  10  centimeters  per  second  in  one 
second. 

EXERCISES.  6.  A  sled  starting  from  rest  runs  down  hill.  Its  initial 
velocity  is  0;  its  velocity  at  the  end  of  the  1st  second  is  6  ft.  per  second; 
at  the  end  of  the  2d  second,  12  ft.  per  second;  at  the  end  of  the  3d  sec- 
ond, 18  ft.  and  so  on.  (a)  What  is  the  increase  in  velocity  per  second? 

(b)  The  positive  acceleration? 

7.  A  stone  is  thrown  upward  with  an  initial  velocity  of  2940  cm.  per 
second.     Its  velocity  at  the  end  of  the  1st  second  is  1960  cm.  per  second; 
at  the  end  of  the  2d  second,  980  cm.  per  second,  and  so  on.     (a)  What 
is  the  decrease  in  velocity  per  second?     (b)  The  negative  acceleration? 

(c)  How  long  will  it  continue  to  rise?     (d)  In  how  many  seconds  after 
leaving  the  hand  will  it  strike  the  ground? 

8.  A  ball  rolling  down  an  incline  makes  a  gain  in  velocity  of  20  cm.  in 
4  seconds.     What  is  the  acceleration? 

36.  Illustrations  of  Accelerated   Motion.     Let  us  consider 
the  case  of  a  marble  starting  from  rest  and  rolling  down  an 
inclined  plane,  Fig.  8.     Suppose  that  the  incline  have  a  pitch 
such  that  the  marble  acquires  at  the  end  of  the  1st  second 
a  velocity  of  2  feet  per  second.     That  is,  starting  from  rest, 
its  velocity  at  the  end  of  the  1st  second  is  2  feet  per  second; 
the  velocity  at  the  end  of  the  2d  second  will  be  4  feet  per 
second;  at  the  end  of  the  3d  second,  6  feet,  and  so  on.     The 
following  points  with  respect  to  the  motion  of  the  marble  may 
be  noted: 


18  HIGH   SCHOOL  PHYSICS 

First }  since  the  body  is  acted  upon  by  a  constant  force  (the 
force  of  gravity)  its  motion  down  the  incline  is  uniformly 
accelerated,  the  gain  in  velocity  (acceleration)  being  2  feet  per 
second  per  second. 


FIG.  8 


Second,  the  average  velocity  for  any  interval  or  number  of 
intervals  may  be  determined  by  taking  one-half  the  sum  of  the 
velocity  at  the  beginning  and  at  the  end  of  the  interval;  that  is, 


average  velocity  =  vdodty  at  6^»^"g  +  *&*%  «* 

2i 

Q     I      2 

Thus,  the  average  velocity  for  the  1st  second  is  —  <j—  =  1 

2  +  4 
foot  per  second;  for  the  2d  second,  —  ~  —  =3;   for   the  3d 

4  +  6 
second,  —  ~  —  =  5,  etc.     In  a  like  manner  we  may  find  the 

average  velocity  for  any  number  of  seconds,  as,  for  example, 

n  i  A 
the  first  3  seconds,  thus,  —  ^—  =  3  feet  per  second. 

Third}  the  space  passed  over  during  any  interval  or  number  of 
intervals  is  equal  to  the  average  velocity  multiplied  by  the 
time.  Thus,  for  the  1st  second  the  average  velocity  is  1  foot 
per  second  and  the  time  1  second,  therefore,  the  space  passed 
over  during  this  second  is  1  foot  ;  for  the  2d  second  the  average 
velocity  is  3  and  the  time  1,  hence  the  space  passed  over  is  3 
feet;  for  the  3d  second  the  average  velocity  is  5,  and  hence  the 
space  passed  over  is  5  feet.  Likewise,  since  the  average 
velocity  for  the  first  3  seconds  is  3  feet  per  second,  and  the 
time  is  3,  the  total  space  passed  over  during  this  interval 
is  9  feet,  and  so  on  for  any  interval  we  may  choose. 


FORCE   AND   MOTION  19 

The  above  facts  may  be  given  in  tabular  form  as  in  the 
following  outline: 

v  ,     ..  Space  per          Total  space 

Time  ycity  second  passed  over 

Beginning  of  time  Vo  =0 0 0 

End  of  1st  second Vi  =2 1 1 

2d       "  V2  =4 3 4 

3d       "  F3  =6 5 9 

4th     "  V,  =  ? ? ? 

5th     "  V6  =? ?. ? 

10th    "  F10  =  ? ? ? 

EXERCISES.  9.  What  is  the  acceleration  of  the  marble?  Is  it  positive 
or  negative? 

10.  What  is  the  velocity  at  the  end  of  the  4th  second?     The  5th  second? 
The  10th  second? 

11.  What  is  the  average  velocity  during  the  4th  second?     The  5th 
second?     The  10th  second? 

12.  What  is  the  average  velocity  during  the  first  4  seconds?     The 
first  5  seconds?     The  first  10  seconds? 

13.  What  is  the  space  passed  over  during  the  4th  second?     The  5th 
second?     The  10th  second? 

14.  What  is  the  space  passed  over  during  the  first  4  seconds?     The 
first  5  seconds?     The  first  10  seconds? 

15.  What  is  the  average  velocity  for  the  interval  (3  seconds)  included 
between  the  end  of  the  1st  second  and  the  end  of  the  4th  second?     What 
space  is  passed  over  during  this  interval? 

37.  Summary.  The  facts  brought  out  in  the  preceding 
topic  with  reference  to  the  accelerated  motion  of  a  body  start- 
ing from  rest  may  conveniently  be  summarized  in  the  follow- 
ing manner.  It  is  evident  that  the  velocity  of  a  body  having 
uniformly  accelerated  motion  may  be  determined  at  the  end  of 
any  interval  by  simply  adding  the  acceleration  to  the  velocity 
at  the  end  of  the  preceding  interval.  Since,  however,  the  accel- 
eration is  constant,  the  most  convenient  way  of  finding  the 
velocity  at  the  end  of  any  interval  is  to  multiply  the  accelera- 
tion by  the  time;  that  is, 


20  HIGH   SCHOOL  PHYSICS 

velocity  =  acceleration  X  time 
v  =  at 

If  now,  we  desire  to  compute  the  space  passed  over  by  a 
body  starting  from  rest,  that  is,  having  an  initial  velocity 
equal  to  0,  and  having  a  velocity  at  the  end  of  t  seconds  equal 
to  at,  we  may  write 

average  velocity  =  — ^—^ 

Since  the  space  passed  over  is  equal  to  the  average  velocity 
multiplied  by  the  time,  we  may  therefore  write 

space  =  average  velocity  x  time 

/  f\     I         /\ 

s  =  (  — £—  J  X  t,  that  is, 
1 


For  a  discussion  of  the  motion  of  bodies  which 
do  not  start  from  rest  but  which  have  an  initial 
velocity,  see  Supplement,  536. 

38.  Falling  Bodies.  Whenever  a  force  acts  upon 
a  body  it  always  tends  to  produce  motion.  A 
stone  dropped  from  the  hand  falls  to  the  earth 
with  an  accelerated  motion  due  to  the  force  of 
gravity.  If  it  were  not  for  the  friction  of  the  air 
all  bodies  would  fall  with  equal  velocities.  If  a 
feather  and  a  coin,  for  example,  be  dropped  from 
a  given  height,  it  will  be  observed  that  the  coin 
will  reach  the  ground  first.  If,  however,  the 
feather  and  coin  be  placed  in  a  tube,  Fig.  9,  and 
the  air  be  exhausted  by  means  of  an  air  pump, 
it  will  be  found  that  both  fall  with  the  same 
velocity,  showing  that  in  a  vacuum  bodies  fall 
with  equal  velocities.  The  acceleration  imparted 
FIG.  9  to  a  freely  falling  body  by  the  force  of  gravity 


FORCE   AND   MOTION  21 

is  represented  by  the  symbol  g.     The  numerical  value  of  this 
acceleration  due  to  gravity  is  approximately  as  follows: 

g  =  32  ft.  per  sec.  per  sec.  =  980  cm.  per  sec.  per  sec. 

This  means  that  if  a  body  start  from  rest  and  fall  freely  under 
the  influence  of  gravity  it  will  have  at  the  end  of  the  1st  sec- 
ond a  velocity  of  32  feet  per  second;  at  the  end  of  the  2d 
second,  64  feet  per  second;  at  the  end  of  the  3d  second,  96  feet 
per  second,  and  so  on:  or  if  this  be  expressed  in  metric  units, 
its  velocity  at  the  end  of  the  1st  second  will  be  980  centimeters 
per  second;  at  the  end  of  the  2d  second,  1960  centimeters  per 
second,  and  so  on. 

The  student  must  bear  in  mind  that  the  values  of  g  given 
above  are  those  which  are  usually  used  in  making  calculations 
involving  the  acceleration  due  to  gravity.  Since  the  force  with 
which  the  earth  attracts  bodies  differs  slightly  from  place  to 
place,  it  follows  that  the  value  of  g  will  be  somewhat  different 
for  different  places,  as  explained  in  Art.  82. 

Falling  bodies  are  subject  to  the  laws  of  accelerated  motion. 
The  equations  for  falling  bodies  starting  from  rest  are  similar 
to  those  already  discussed  in  Art.  37. 

v  =  gt 
s  =  \  g? 

EXERCISES.  16.  Suppose  that  a  sled  start  from  rest  on  a  hillside  and 
move  downward  with  an  acceleration  of  3  ft.  per  second,  (a)  What 
will  be  its  velocity  at  the  end  of  10  seconds?  (b)  At  the  end  of  1 
minute? 

17.  (a)  Over  what  space  will  the  sled  pass  during  the  10  seconds? 
(b)  During  the  first  minute? 

18.  A  body  starting  from  rest  falls  for  10  seconds.     Find  its  velocity 
at  the  end  of  this  time  in   (a)  feet   per  second;    (b)   centimeters  per 
second. 

19.  How  far  will  the  body  fall  during  the  10  seconds  in  (a)  feet?    (b) 
centimeters? 


22  HIGH  SCHOOL  PHYSICS 

NEWTON'S  LAWS  OF  MOTION 

39.  Laws  of  Motion.     The  relation  between  force  and  motion 
is  expressed  by  three  important  laws  known  as  Newton's  laws 
of  motion.     These  laws  were  formulated  by  Sir  Isaac  Newton 
(1642-1727),  a  'famous  English  mathematician  and  physicist, 
and   upon  them  is  based  some  of  the  most  important  prin- 
ciples of  modern  mechanics.     The  three  laws  of  motion  are 
as  follows: 

I.  Every  body  tends  to  preserve  its  state  of  rest  or  of  uniform 
motion  in  a  straight  line  unless  compelled  by  some  external  force 
to  change  that  state. 

II.  Change  of  motion  is  proportional  to  the  impressed  force, 
and  takes  place  in  the  direction  in  which  the  force  acts. 

III.  To  every  action  there  is  an  equal  and  opposite  reaction. 

40.  Inertia.     Newton's   first   law  of  motion   is   sometimes 
called  the  law  of  inertia.     Inertia  is  that  property  of  matter  by 
virtue  of  which  a  body  at  rest  tends  to  remain  at  rest,  and  when  in 
motion  tends  to  continue  in  motion  in  a  straight  line.     Inertia  is 
the  inability  of  a  body,  of  itself,  to  change  its  state  of  rest  or 
motion.     A  book  lying  on  a  table  will,  by  virtue  of  its  inertia, 
lie  there  forever  unless  acted  upon  by  some  external  force; 
likewise,  a  stone  thrown  upward  will,  by  virtue  of  its  inertia, 
move  out  into  space  in  a  straight  line  if  not  acted  upon  by  some 
outside  force,  as  for  example,  the  force  of  gravity. 

41.  Illustrations    of    Inertia.     Experiment.     Place    a    coin 
upon  a  card  resting  on  the  end  of  a  rod  clamped  to  the  table, 
Fig.  10.     If  the  card  be  snapped  sharply  with  the  finger,  it  will 
fly  out,  leaving  the  coin  in  place  on  the  end  of  the  rod.     The 
coin  remains  stationary  because  of  its  inertia.     Other  illus- 
trations are  seen  in  the  jerking  of  a  sled  from  beneath  a  child 
sitting  upon  it;  the  forward  motion  of  a  person  in  a  car  when 
it  suddenly  comes  to  rest;   the  hammering  of  water  in  water 
pipes  when  the  faucet  is  suddenly  closed;  the  stamping  of  snow 


FORCE   AND   MOTION 


23 


from  the  feet.  An  interesting  illustration  of  inertia  is  that  of 
the  motion  of  a  circus  rider  in  jumping  over  a  line  as  shown  in 
Fig.  11.  All  the  rider  has  to  do  in  order  to  perform  his  act  is 


FIG.  10 


FIG.  11 


to  jump  high  enough  to  clear  the  line,  the  inertia  of  his  body 
carrying  him  forward  so  that  he  lands  again  squarely  upon  the 
horse. 

42.  Momentum.  The  second  law  of  motion  may  be  called 
the  law  of  momentum.  Momentum  is  the  quantity  of  motion 
which  a  moving  body  possesses. 


Momentum  =  mass  X  velocity 


mv. 


There  is  no  generally  accepted  name  given  to  the  unit  of 
momentum.  (Supplement,  537.)  We  may  say,  for  example, 
that  the  momentum  of  a  mass  of  10  pounds  moving  with  a 
velocity  of  10  feet  per  second  is  10  X  10  =  100.  Also,  the 
momentum  of  a  mass  of  10  tons  moving  with  a  velocity  of  10 
yards  per  second  is  10  X  10  =  100.  If,  however,  we  wish  to 
compare  the  momenta  of  the  two  bodies,  it  is  necessary  to 
reduce  the  factors  of  mass  and  velocity  to  some  common  unit. 
Thus,  in  the  case  given  above,  the  momentum  of  the  first 
body,  in  terms  of  pounds  and  feet,  is  10  X  10  =  100;  the 
momentum  of  the  second  body,  expressed  in  the  same  units, 
-is  20,000  X  30  =  600,000.  The  momentum  of  a  body  may  be 
changed  by  changing  its  mass  or  velocity,  or  both. 

43.  Further  Illustrations  of  the  Second  Law  of  Motion.  An 
interesting  illustration  of  the  second  law  of  motion  is  that  seen 


24 


HIGH   SCHOOL  PHYSICS 


FIG.  12 


in  the  effect  of  the  force  of  gravity  on  a  projectile,  as  shown  in 
Fig.  12.  Suppose  that  a  ball  is  fired  horizontally  from  a  cannon, 
and  at  the  same  instant  a  similar  ball  is  dropped  vertically 
downward.  Since  a  force  has  the  same  effect  in  producing 
motion  whether  the  body  upon  which  it  acts  is  at  rest  or  in 

motion,  or  whether  the 
body  is  acted  upon  by 
that  force  alone  or  by 
other  forces  at  the 
same  time,  it  follows 
that  both  balls  will 
reach  the  ground  si- 
multaneously. 

44.  Action  and  Re- 
action. The  third  law 
of  motion  states  that 
to  every  action  there 
is  an  equal  and  oppo- 
site reaction;  that  is,  every  force  is  two  sided  in  its  nature.  If 
we  push  on  a  wall  with  a  given  force,  the  wall  reacts  (pushes 
back)  with  an  equal  force.  In  rowing  a 
boat  we  act  on  the  water,  and  the  water 
in  turn  reacts  on  the  boat,  causing  it  to 
move.  The  bird  in  flying  acts  on  the  air 
with  its  wings;  the  air  reacts  on  the  bird, 
giving  it  motion. 

An  excellent  illustration  of  action  and 
reaction  is  that  seen  in  the  case  of  the  ro- 
tating lawn  sprinkler.  The  water  in  flow- 
ing from  the  sprinkler,  Fig.  13,  reacts  upon  the  curved  arms, 
causing  them  to  rotate.  The  action  of  the  sprinkler  is  exactly 
similar  to  that  which  occurs  when  a  person  attempts  to  jump 
from  a  light  boat  to  the  shore.  As  the  person  jumps  forward 
(action)  he  kicks  the  boat  backward  (reaction). 

EXERCISE.     20.   Would  a  rotating  lawn  sprinkler  work  in  a  vacuum? 


FIG.  13 


FORCE   AND   MOTION 


25 


45.  Relation  of  Action  and  Reaction  to  Momentum.  The 
terms  action  and  reaction  may  be  interpreted  to  mean  momen- 
tum. (Supplement,  538.)  For  example,  when  the  powder  in 
a  gun  explodes  it  acts  upon  both  the  bullet  and  the  gun  with 
equal  force.  The  momentum  of  the  gun  is  equal  to  the  momen- 
tum of  the  bullet.  This  relation  of  action  to  reaction  may  be 
expressed  by  an  equation  as  follows: 

mv  =  m'v' 

in  which  m  and  v  equal  the  mass  and  velocity  of  the  gun,  and 
m'  and  v'  the  mass  and  velocity  of  the  bullet.  The  velocity  of 
the  bullet  will  be  as  many  times  greater  than  the  velocity  of 
the  gun  as  the  mass  of  the  gun  is  greater  than  the  mass  of  the 
bullet.  The  lighter  the  gun,  therefore,  the  greater  its  "kick" 
or  recoil.  If  bullet  and  gun  were  of  equal  masses  they  would 
fly  apart,  when  the  powder  explodes,  with  equal  velocities. 


FIG.  14 


FIG.  15 


EXERCISES.  21.  Suppose  that  a  ball  of  mass  1  Ib.  is  fired  from  a  cannon 
of  mass  1  ton,  with  a  velocity  of  1000  ft.  per  second.  What  will  be  the 
velocity  of  the  gun's  recoil? 

22.  When  an  apple  falls  to  the  earth  its  momentum  toward  the  earth, 
according  to  the  third  law  of  motion,  is  equal  to  the  momentum  of  the 
earth  toward  the  apple.     How  does  the  velocity  of  the  earth  compare  with 
that  of  the  apple? 

23.  A  boy  pulls  on  a  rope,  as  shown  in  Fig.  14,  with  a  force  of  50  Ibs.,  as 
registered  by  the  spring  balance  S.     (a)  What  force  is  exerted  on  the  rope? 
(b)  What  force  is  exerted  on  the  post? 

24.  If  a  second  boy  take  the  place  of  the  post,  Fig.  15,  and  each  pull 
with  a  force  of  50  Ibs.,  what  will  b'e  the  reading  of  the  spring  balance? 


26 


HIGH   SCHOOL  PHYSICS 


UNITS  OF  FORCE 

46.   Force  Measured  by  a  Spring  Balance.     One  of  the  most 
usual  methods  of  measuring  the  pull  which  a  force  exerts  is  by 
means  of  the  spring  balance,  or  dynamometer  as  it 
is  sometimes  called,  Fig.  16. 

Experiment.  Attach  to  the  hook  of  a  spring  bal- 
ance a  given  mass.  The  pointer  of  the  instrument 
moves  to  a  certain  position  on  the  scale.  This  indi- 
cates, in  pounds  or  grams  as  the  case  may  be,  the 
force  with  which  tne  earth  attracts  the  body.  Now, 
attach  the  hook  of  the  balance  to  some  object,  say  a 
nail  or  a  hook  in  the  wall,  and  pull  upon  it.  The 
reading  of  the  instrument  again  indicates  the  magni- 
tude of  the  force  exerted. 

47.  Force  Measured  by  the  Product  of  Mass  and 
Acceleration.  The  force  exerted  upon  a  given  mass 
may  also  be  measured  by  the  acceleration  which  is 
imparted  to  it.  This  is  the  method  usually  em- 
ployed in  scientific  determinations  of  the  magnitude 
of  a  force.  To  thus  determine  the  magnitude  of 
a  force  acting  upon  a  body  it  is  necessary  to  know 
the  mass  of  the  body  and  its  acceleration.  The  product  of 
these  two  factors  is  a  measure  of  the  force;  that  is,  F  =  ma. 

48.  Units  of  Force.  The  units  employed  in  this  country  are 
of  two  kinds:  (a)  the  gravitational  units  and  (b)  the  absolute 
units,  each  being  measured  in  terms  of  both  the  English  and 
the  metric  systems.  The  gravitational  units  are  used  in  nearly 
all  ordinary  practical  measurements;  the  absolute,  in  accurate 
scientific  measurements.  The  following  outline  may  be  of  serv- 
ice in  making  clear  the  relation  of  the  two  sets  of  units. 


FIG.  16 


Units  of  force 


gravitational 


absolute 


I  pounds  of  force 
( grams  of  force 
I  poundals 


FORCE  AND   MOTION  27 

49.  Gravitational   Units   of  Force.     The  gravitational  units 
of  force  are  those  which  compare  the  push  or  the  pull  exerted  by  a 
force  with  the  attraction  due  to  gravity.     The  English  gravita- 
tional unit  is  the  weight  of  a  pound  (also  called  the  force  of  a 
pound) .     The  weight  of  a  pound  is  a  force  equivalent  to  the  attrac- 
tion of  the  earth  for  a  pound  of  mass.     (Supplement,  539.)     The 
force  of  a  gram  (weight  of  a  gram)  is  a  force  equivalent  to  the  attrac- 
tion of  the  earth  for  a  gram  mass.     Since  the  attraction  of  the 
earth  for  a  given  mass  varies  slightly  for  different  places,  the 
gravitational  units  of  force  likewise  vary.     This  variation  for 
ordinary  practical  measurements,  however,  is  so  small  as  to  be' 
negligible. 

50.  Absolute  Units  of  Force.     The  absolute  units  of  force, 
the  poundal  and  the  dyne,  are  derived  from  the  product  of  the 
mass  of  a  body  and  the  acceleration  imparted  to  it.     The 
poundal  is  that  force  which  will  give  to  a  pound  mass  an  acclera- 
tion  of  one  foot  per  second  per  second.     The  dyne  is  that  force 
which  will  give  to  a  gram  mass  an  acceleration  of 'one  centimeter 
per  second  per  second.     Since  the  absolute  units  are  used  pri- 
marily in  making  accurate  scientific  measurements,  it  is  not 
highly  important,  in  an  elementary  work  on  physics,  that  this 
subject  receive  special  attention.     Two  things  with  respect  to 
the  absolute  units,  however,  are  important   for  the  student 
to  keep  in  mind;  namely,  (a)  that  in  accurate  scientific  meas- 
urements the  absolute  units  are  used,  and  (b)  that  from  the 
absolute  units  there  are  derived  some  of  our  most  common 
practical  units,  such  as  the  watt  and  the  kilowatt. 

51.  The  Relation  of  Absolute  to  Gravitational  Units.     The 
relation  of  gravitational  to  absolute  units  (Supplement,  540) 
may  be  expressed,  approximately,  as  follows: 

1  pound  of  force  =  32  poundals 
1  gram  of  force    =  980  dynes 

EXERCISES.  25.  A  mass  of  10  grams  held  in  the  hand  exerts  upon  the 
hand,  due  to  the  attraction  of  the  earth,  a  force  of  10  grams.  What  is  the 
force  in  dynes? 


28  HIGH   SCHOOL  PHYSICS 

26.  A  mass  of  1  kilogram  rests  upon  the  table.     What  force  does  it 
exert  upon  the  table  in  (a)  grams  of  force?    (b)  dynes? 

27.  A  magnet  exerts  a  force  of  6860  dynes  on  a  piece  of  iron.     Find  the 
force  in  grams. 

COMPOSITION  AND  RESOLUTION  OF  FORCES 

52.  Graphic    Representation    of   Forces.     A   force   is   fully 
described  when  we  know  three  things  about  it;  namely,  (a)  its 
point  of  application,  (b)  its  magnitude,  and  (c)  its  direction. 
(Supplement,  541.)     Thus,  when  we  say,  "A  force  of  10  pounds 
acts  vertically  downward  on  a  body,"  we  fully  describe  the 
force,  because  we  designate  its  point  of  application,  its  mag- 
nitude (10  Ibs.),  and  its  direction  (downward). 

Forces,    velocities,   and   accelerations   may   be   represented 
graphically  by  means  of  lines.     Thus,  the  line  AB,  Fig.  17, 
*  r>    represents  a  force  acting  from  A  to  B. 

— >•  If  we  let  a  length  of  one  inch  represent  a 
force  of  10  pounds,  then  a  line  6  inches  in 
length  will  represent  a  force  of  60  pounds. 
Likewise,  a  velocity  of  20  miles  per  hour 
in  a  northeasterly  direction  ,may  be  rep- 
resented in  magnitude  and  direction  by  a 
line  20  centimeters  in  length  drawn  from 
F  18  A  to  D,  as  shown  in  Fig.  18.  When 

drawing  upon  the  blackboard,  the  inch 
may  conveniently  be  used  as  the  scale  unit;  when  drawing 
upon  paper,  the  centimeter,  or  in  some  cases  the  millimeter, 
is  the  unit  usually  employed. 

53.  Composition  of  Forces.     If  two  or  more  forces  act  upon 
a  body  at  the  same  time  the  resultant  force  may  be  determined 
graphically.     The  various  forces  acting  upon  a  body  are  called 
components;    a  single   force  which  acting  alone  will  produce 
the  same  result  as  the  components  is  called  the  resultant.     The 
process  of  finding  the  resultant  of  a  number  of  forces  is  called 
the  composition-  of  forces.     We  may  in  a  like  manner  speak  of 


FORCE  AND   MOTION  29 

the  composition  of  velocities  and  accelerations.  In  the  com- 
position of  forces,  velocities,  and  accelerations  there  are  a  num- 
ber of  important  cases  which  are  considered  in  an  elementary 
manner  in  the  following  topics. 

54.  Parallel  Forces  in  the  Same  Straight  Line.     The  result- 
ant of  two  or  more  forces  acting  in  the  same  straight  line  is 
equal  to  the  algebraic  sum  of  the  forces.     Components  acting 
to  the  right  or  upward  from  a  given  point  are  said  to  have  the 
plus  sign;  those  acting  downward,  or  to  the  left,  the  minus  sign. 

EXERCISES.  28.  If  a  man  on  top  of  a  freight  car,  which  moves  with  a 
velocity  of  30  ft.  per  second,  run  in  the  direction  in  which  the  car  is  moving, 
with  a  velocity  of  10  ft.  per  second,  what  is  the  resultant  (actual)  velocity 
of  the  man? 

29.  Suppose  that  the  man  run  in  the  opposite  direction  with  a  velocity 
of  10  ft.  per  second.     What  will  be  the  resultant  velocity? 

30.  Three  forces,v  one  due  to  the  tide,  one  due  to  the  wind,  and  the 
third  the  force  exerted  by  the  engine,  act  in  the  same  straight  line  upon  a 
boat.     The  tide  acts  to  the  westward  with  a  force  of  4  units;   the  wind 
acts  in  the  same  direction  with  a  force  of  12  units;   the  engine  drives  the 
boat  to  the  eastward  with  a  force  of  50  units.     Find  the  magnitude  and 
direction  of  the  resultant. 

55.  Parallel  Forces  not  in  the  Same  Straight  Line.     The 
resultant  of  two  forces  acting  in  the  same  direction  but  not  in 
the  same  straight  line  is  equal  to  the  sum  of  the  forces,  and 
the  point  of  application  of  the  resultant  divides  the  distance 
between  the  forces  into  lengths  inversely  proportional  to  the 
forces. 

Experiment.  This  principle  may  be  illustrated  by  means 
of  two  spring  balances 
and  a  weight,  Fig.  19. 
Let  a  given  weight  W 
(12  Ibs.,  for  example) 
be  suspended  at  such 
a  point  B  that  the 
force  on  the  spring 
balance  S  is  4  pounds  FIG.  19 


30 


HIGH   SCHOOL  PHYSICS 


and  the  force  on  S'  8  pounds.  The  resultant  W  equals  4  +  8 
=  12.  The  relation  of  the  two  arms  AB  and  BC  may  be 
expressed : 

AB:BC  =  8:4 

It  is  important  to  note  that  the  greater  force  (8)  is  on  the 
side  of  the  short  arm,  and  the  lesser  force  (4)  is  on  the  side  of 
the  long  arm. 


FIG.  20 


FIG.  21 


EXERCISES.  31.  If  W,  Fig.  19,  exert  a  force  of  20  Ibs.,  what  will  be 
the  force  on  S  and  on  Sf  if  W  be  placed  (a)  midway  between  A  and  C  ? 
(b)  i  of  the  distance  from  A?  (c)  I  of  the  distance  from  C? 

32.  Two  boys,  Fig.  20,  carry  between  them  a  block  of  ice  weighing 
90  Ibs.     The  distance  AB  is  2  ft.  and  the  distance  AC  is  4  ft.     Find  what 
part  of  the  load  each  boy  carries. 

33.  A  mass  of  600  Ibs.  rests  on  a  beam  AB,  9  ft.  in  length,  Fig.  21,  at  a 
distance  3  ft.  from  B.     How  much  does  each  support  carry,  neglecting  the 
weight  of  the  beam? 

34.  If  AC,  Fig.  19,  be  100  cm.  in  length,  where  must  a  weight  of  300 
grams  be  placed  so  that  the  force  exerted  on  S  shall  be  75  grams  and  on 
S'  225  grams.     Note.  —  Let  x  equal  the  long  arm  AB  and  (100  —  x  )  equal 
the  short  arm. 

56.  Forces  Making  an  Angle  with  Each  Other.  The  result- 
ant of  two  forces  making  an  angle  with  each  other  is  equal  to 
the  diagonal  of  the  parallelogram  formed  by  the  lines  repre- 
senting the  forces  as  sides. 

Two  cases  are  to  be  considered.  First,  when  the  angle 
formed  by  the  components  is  a  right  angle,  Fig.  22,  and  sec- 


FORCE  AND   MOTION 


31 


ond,  when  the  angle  formed  by  the  components  is  not  a  right 
angle,  Fig.  23.  In  the  first  case  the  resultant  R  is  the  hypothe- 
nuse  of  a  right  angled  triangle,  and  we  may  write  R  =' 
+  AC2.  In  the  second  case  three  methods  of  find- 


FIG. 22 


FIG.  23. 


ing  the  resultant  are  possible:  (a)  By  experiment  with  spring 
balances;  (b)  by  the  graphic  method;  and  (c)  by  the  use  of 
trigonometry.  In  elementary  texts  only  the  first  two  methods 
are,  in  general,  employed. 

57.  Experimental  Determination  of  the  Resultant.  Experi- 
ment. Suspend  two  spring  balances  C  and  D  from  hooks  in 
the  frame  of  the  black- 
board, and  attach  to 
them  a  weight  W,  Fig. 
24.  Lay  off  on  the 
board  the  line  Ac  equal 
in  inches  to  the  numeri- 
cal reading  of  the  balance 
C;  lay  off  another  line 
Ad  numerically  equal  in 
inches  to  the  reading  of 
the  balance  D.  Now 
complete  the  parallelo- 
gram, and  the  diagonal 
A  B  will  represent  in  di- 
rection and  magnitude  the 


FIG.  24 


resultant     in 
weight  W. 


inches    should 


resultant.     The 
be    numerically 


value   of   this 
equal    to   the 


32 


HIGH  SCHOOL  PHYSICS 


58.  Graphic   Method   of  Finding  the  Resultant.      To   find 
the  resultant  of  two  components  which  act  upon  a  body  at 
a  given  angle.     Suppose  that  A  represents  a  boat  on   the 
surface  of  the  lake,  and  that  it  is  acted  upon  by  two  forces, 
the  wind  and  the  tide.     The  wind  tends  to  give  it  a  velocity 
in  the  direction  A B  of  20  feet  per  minute;  the  tide,  acting  at 
an  angle  of  60°  to  the  direction  of  the  wind,  tends  to  give  it  a 
velocity  of  15  feet  per  minute.     We  wish  to  find  the  direction 
and  magnitude  of  the  resultant  velocity.     In  other  words,  we 

wish  to  find  the  actual  direc- 
tion and  velocity  of  the  boat. 
Lay  off  on  paper  a  line  A  B  20 
centimeters  in  length  to  rep- 
resent a  velocity  of  20  feet. 
From  the  point  A,  Fig.  25,  lay 
off  AC  15  centimeters  in  length, 
making  with  AB  an  angle  of 

60°.  Now  complete  the  parallelogram.  The  line  AD  repre- 
sents the  magnitude  and  direction  of  the  resultant,  its  length 
in  centimeters  being  numerically  equal  to  the  velocity  of  the 
boat  in  feet  per  minute. 

When  more  than  two  components  are  given,  the  resultant 
may  be  determined  by  repetition  of  the  parallelogram  of 
forces.  (Supplement,  542.) 

59.  Resolution    of    Forces.     In  the  cases  just   considered, 
namely,  those  dealing  with  the  composition  of  forces  or  veloci- 
ties, the  components  were  given  to  find  the  resultant.     When, 
on  the  other  hand,  the  resultant  is  given  to  find  the  com- 
ponent, the  process  is  called  the  resolution  of  forces  or  ve- 
locities,  as  the    case   may   be.      This  problem   requires   the 
construction  of    a  parallelogram  having  the  given  resultant 
as  its  diagonal. 

Example.  Suppose  that  the  resultant  of  two  forces  acting 
at  right  angles  to  each  other  is  100  dynes.  The  resultant 
makes  an  angle  of  30°  with  one  of  the  forces!  Find  the  mag- 


FORCE  AND   MOTION 


33 


nitude  of  the  forces.  Solution :  Draw  two  lines  A  X  and  A  Y 
at  right  angles  to  each  other,  Fig.  26.  From  the  point  A 
draw  the  line  AD,  making  an  angle  of  30°  with  AX  and  having 
a  length  of  10  centimeters,  each  centimeter  representing  10 
dynes.  The  line  AD  represents  the  resultant  (100  dynes)  in 
magnitude  and  direction.  Now  from  the  point.  D  draw  a  line 
DB  parallel  to  AY]  also  from  D  draw  the  line  DC  parallel  to 
AX.  The  lines  AB  and  AC  represent  the  magnitude  and 
direction  of  the  components  sought. 


FIG.  26 


FIG.  27 


EXERCISE.  35.  A  boy  pushes  a  lawn  mower  with  a  force  of  50  Ibs., 
the  force  acting  in  the  direction  of  the  handle,  which  makes  an  angle  of 
30°  with  the  horizontal,  Fig.  27.  Find,  by  drawing,  what  part  of  the  force 
acts  (a)  horizontally,  and  (b)  vertically.  ^«MM 

For  further  discussion  of  the  subject  of  Resolution  of  Forces, 
see  Supplement,  543. 

EXERCISES  AND  PROBLEMS  FOR  REVIEW 

1.  Define:  Motion,  velocity,  acceleration.     Give  illustration  of  posi- 
tive acceleration;    negative  acceleration. 

2.  Explain  the  use  of  the  following  equations,  and  explain  the  mean- 
ing of  each  term:   v  =  at ;   s  =  %  at2;   s  =  %  gtz. 

3.  A  body  acted  upon  by  a  constant  force  starts  from  rest  and  at  the 
end  of  the  1st  second  has  a  velocity  of  5  ft.  per  second;   at  the  end  of  the 
2d  second  10  ft.  per  second,  and  so  on.     What  is  its  velocity  (a)  at  the  end 
of  5  seconds?    (b)  5  minutes? 

4.  (a)  Over  what  space  does  the  body  (problem  3)  pass  in  10  seconds? 
(b)  in  1  minute? 


34  HIGH  SCHOOL  PHYSICS 

6.   How  far  does  it  go  during  the  10th  second? 

6.  A  force  acting  upon  a  body  causes  it  to  change  its  velocity  from  0 
to  20  ft.  per  second  during  the  first  5  seconds.  How  far  will  it  move  under 
the  action  of  this  force  in  20  seconds? 

••  7.  A  body  falls  from  rest  for  10  seconds.  Over  what  space,  in  feet, 
does  it  pass  (a)  during  the  first  5  seconds  of  its  fall?  (b)  during  the  last 
5  seconds? 

8.  Solve  problem  7  in  metric  units,  using  g  =  980  cm.  per  second  per 
second. 

9.  A  body  is  thrown  upward  with  a  velocity  of  320  ft.  per  second, 
(a)  For  how  many  seconds  will  it  rise?   (b)  How  high  will  it  rise? 

10.  Define:   Force,  pound  of  force,  gram  of  force,  poundal,  dyne. 

11.  (a)  A  force  of  10  Ibs.  is  equivalent  to  how  many  poundals?   (b)  A 
force  of  640  poundals  is  equivalent  to  how  many  pounds  of  force? 

12.  A  mass  of  245  grams  is  acted  upon  by  a  force  which  imparts  to 
it  an  acceleration  of   8   cm.  per  second  per  second.     Find  the  force  in 
(a)  dynes;    (b)  grams  of  force. 

13.  Define  and  illustrate:  Inertia,  momentum. 

14.  Explain  each  term  of  the  equation  mv  =  m'v',  and  explain,  also,  to 
what  law  of  motion  it  applies. 

15.  Compare  the  momentum  of  a  body  having  a  mass  of  2  ounces  and 
a  velocity  of  40  ft.  per  second  with  that  of  a  body  having  a  mass  of  2  Ibs. 
and  a  velocity  of  2  ft.  per  second. 

16.  A  shot  is  fired  from  a  cannon  having  a  mass  of  1  ton.    The  velocity 
of  the  shot  is  1000  ft.  per  second,  that  of  the  cannon  2  ft.  per  second. 
Find  the  mass  of  the  shot. 

17.  Explain  the  terms   (a)  composition  of  forces;    (b)  resolution  of 
forces.     To  what  other  physical  quantities  may  the  principles  of  compo- 
sition and  resolution  apply? 

18.  A  12  ft.  plank  spans  a  stream.     A  man  weighing  200  Ibs.  crosses 
on  the  plank.     Call  one  end  of  the  plank  A  and  the  other  B,  and  assume 
that  the  man  walks  from  A  toward  B.    What  part  of  his  weight  rests 
upon  each  support  when  he  is  (a)  4  ft.  from  A?   (b)  6  ft.  from  A?   (c)  8  ft. 
from  A? 

19.  A  boy  draws  a  sled  by  means  of  a  rope  which  makes  an  angle 
of  40°  with  the  horizontal.     He  exerts  on  the  rope  a  force  of  30  Ibs. 

(a)  What  is  the  horizontal  component  of  this  force  acting  upon  the  sled? 

(b)  The  vertical  component?     Make  drawing  to  illustrate  the  solution  of 
this  problem. 

20.  A  stream,  which  is  a  mile  wide,  flows  with  a  velocity  of  one  mile  per 
hour.     A  man  at  A  on  one  side  desires  to  cross  to  B,  which  lies  exactly 
opposite  A.     The  man  steers  his  boat  directly  across  stream  and  rows  at 


FORCE  AND   MOTION  35 

the  rate  of  one  mile  an  hour,  (a)  Where,  with  reference  to  B,  will  he  land? 
(b)  If  he  directs  his  boat  up  stream  to  a  point  one  mile  above  B,  and  rows 
until  he  reaches  the  opposite  shore,  where  will  he  land?  (c)  If  he  heads 
his  boat  directly  up  stream  and  rows  for  an  hour,  where  will  he  be  at  the 
end  of  that  time? 

For  additional  Exercises  and  Problems,  see  Supplement. 


CHAPTER  III 


MECHANICS    OF    SOLIDS 

CENTRIFUGAL  FORCE  AND  ITS  APPLICATIONS 

60.  Centrifugal  Force.  Experiment.  If  a  small  mass  be 
attached  to  a  string  and  whirled  rapidly  around,  a  distinct  pull 
on  the  string  will  be  felt,  becoming  greater  as  the  velocity  of  the 
rotating  body  increases.  This  pull  on  the  string  is  due  to  the 
tendency  of  the  rotating  body  to  obey  the  first  law  of  motion; 
that  is,  it  tends  to  fly  off  in  a  straight  line.  The  force  which 
keeps  the  body  from  flying  off  in  a  straight  line  and  which  acts 
along  the  string  toward  the  center  of  rotation  is  called  the 
centripetal  force;  the  reaction  of  the  body  against  being  pulled 
out  of  a  straight  line  is  the  centrifugal  force.  Centripetal  force 
acts  toward  the  center  of  rotation;  centrifugal  force  is  directed 
away  from  the  center.  These  forces  are  equivalent  to  action 
and  reaction;  they  are  equal  to  each  other  in  magnitude,  and 
act  in  opposite  directions. 


FIG.  28 


FIG.  29 


61.   Illustrations    of    Centrifugal   Force.     Experiments   with 
whirling  table. 


MECHANICS  OF   SOLIDS  37 

1.  If  some  mercury  and  water  be  placed  in  a  receptacle  and 
rotated  rapidly,  the  mercury  will  take  a  position  in  the  equa- 
torial region  of  the  globe,  with  the  water  on  either  side,  Fig. 
28.     The  mercury,  having  a  greater  mass  per  unit  of  volume 
than  that  of  the  water,  exerts  a  greater  centrifugal  force,  and 
hence  gets  farthest  from  the  axis  of  rotation.     This  experi- 
ment illustrates  the  principle  of  the  modern  cream  separator, 
by  means  of  which  the  cream  is  separated  from  the  milk. 

2.  If  a  circular  band  of  metal  be  whirled  about  a  central 
axis,  Fig.  29,  it  will  flatten  at  the  poles,  due  to  the  fact  that 
the  particles  in  the  region  a  have  a  greater  velocity,  and  hence 
exert  a  greater  centrifugal  force  than  do  the  particles  in  the 
region  of  the  poles  b. 

62.  Other  Illustrations  of  Centrifugal  Force.     Further  illus- 
trations of  the  action  of  centrifugal  force  may  be  seen  in  the 
ordinary  affairs  of  everyday  life.      For  example,  the 

water  on  a  grindstone  and  the  mud  on  the  carriage 
wheel  are  thrown  off  due  to  the  centrifugal  force 
exerted  by  the  rotating  bodies.  Water  in  a  pail 
may  be  whirled  around  in  a  vertical  plane,  Fig.  30. 
In  this  case  the  water  is  kept  in  the  pail  by  the  cen- 
trifugal force  tending  to  throw  it  away  from  the  cen- 
ter. Also,  a  bicycle  rider  in  going  around  a  corner 
instinctively  leans  inward  to  overcome  centrifugal 
force,  which  tends  to  overturn  him.  For  the  same 
reason  the  circus  rider  leans  in  toward  the 'center  of 
the  ring.  Likewise,  on  railway  curves  the  outer  rail 
is  laid  higher  than  the  inner  rail  to  overcome  the 
centrifugal  force  exerted  by  the  train.  Centrifugal  machines 
for  the  drying  of  salt,  sugars,  and  even  clothes  by  rapid  rota- 
tion are  now  in  common  use. 

63.  Laws   of   Centrifugal   Force.     The   laws   of   centrifugal 
(also  centripetal)  force  are  as  follows: 

I.    Centrifugal  force  is  proportional  to  the  mass  of  the  rotating 
body.     That  is,  the  greater  the  mass  the  greater  the  force.     For 


38  HIGH   SCHOOL  PHYSICS 

example,  if  a  mass  of  1  pound  be  whirled  around  with  a  given 
velocity,  a  given  centrifugal  force  (pull  on  the  string)  will  be 
exerted;  if,  now,  a  mass  of  10  pounds  be  rotated  with  the  same 
linear  velocity,  the  centrifugal  force  will  be  10  times  as  great 
as  in  the  first  case. 

II.  Centrifugal  force  is  directly  proportional  to  the  square  of 
the  velocity.     If  the  velocity  of  the  rotating  body  be  increased 
from  1  foot  per  second  to  10  feet  per  second,  the  centrifugal 
force  will  be  increased  from  1  to  100. 

III.  Centrifugal  force  is  inversely  proportional  to  the  radius 
of  rotation. 

These  three  laws  may  be  expressed  by  means  of  an  equation, 

F-— 

r 

in  which  F  is  the  force,  m  the  mass  of  the  rotating  body, 
v  the  velocity,  and  r  the  radius  of  rotation.  This  equation 
expresses  the  force  in  absolute  units. 

Example.  A  mass  of  4  pounds  is  whirled  around  at  the  end 
of  a  string  2  feet  in  length  with  a  linear  velocity  of  4  feet  per 
second.  Find  the  pull  on  the  string  due  to  rotation  in  (a) 

poundals;    (b)  pounds.     Solution:  C.F.  = =  -        -  =  32 

r  4 

poundals  =  1  pound  of  force. 

EXERCISE.  1.  A  mass  of  98  grams  attached  to  the  end  of  a  string 
10  cm.  in  length  is  whirled  around  with  a  velocity  of  10  cm.  per  second. 
Find  the  centrifugal  force  exerted  by  the  rotating  body  in  (a)  dynes;  (b) 
grams  of  force. 

GRAVITATION,  GRAVITY,  CENTER  OF  GRAVITY,  STABILITY 

64.  Gravitation.  Gravitation  is  the  force  with  which  every 
particle  of  matter  in  the  universe  attracts  every  other  particle.  The 
law  of  universal  gravitation  was  first  announced  by  Newton 
as  follows:  Every  body  attracts  every  other  body  with  a  force 
porportional  to  the  product  of  their  masses  and  inversely  pro- 


MECHANICS   OF   SOLIDS  39 

portional  to  the  square  of  the  distance  between  their  centers. 
This  law  may  be  written 


in  which  F  is  the  force  of  gravitation,  measured  usually  in 
pounds  or  dynes;  m  and  mf  are  the  masses  of  the  bodies;  d  is 
the  distance  between  their  centers ;  and  fc  is  a  constant  depend- 
ing on  the  kind  of  unit  employed.  (Supplement,  544.) 

By  assuming  the  truth  of  this  general  law  of  gravitation, 
astronomers  have  been  enabled  to  describe  accurately  the  motion 
of  the  heavenly  bodies,  as,  for  example,  to 'predict  eclipses,  the 
return  of  comets,  and  to  discover  new  planets. 

65.  Gravity.    Gravity  is  the  attraction  which  exists  between  the 
earth  and  other  bodies.     Gravitation  is  a  general  term,  referring 
to  the  universal  attraction  which  exists  between  all  bodies; 
gravity  is  a  specific  term,  referring  to  the  attraction  of  the 
earth  for  bodies  usually  considered  at  or  near  its  surface. 

66.  The  Relation  of  the  Weight  of  a  Body  to  its  Position  on 
the  Earth.     Since  the  weight  of  a  body  is  the  measure  of  the 
force  of  gravity  acting  upon  it,  and  since  the  force  of  gravity 
for  a  given  mass  varies  for  different  positions  with  respect  to 
the  earth's  surface,  it  follows  that  the  weight  of  a  body  may 
vary  from  place  to  place.     The  relation  of  weight  with  refer- 
ence to  the  earth's  surface  may  be  stated  briefly  as  follows: 

1.  Weight  at  the  surface.     The  nearer  a  body  is  to  the  cen- 
ter of  the  earth,  so  long  as  it  remains  upon  the  surface,  the  greater 
is  its  weight.     Thus  a  given  mass  will  weigh  more  at  the  base 
of  a  mountain  than  at  the  top;   also,  since  the  polar  radius  of 
the  earth  is  13  miles  less  than  the  equatorial  radius,  and  there- 
fore a  body  at  the  poles  is  nearer  the  center  of  the  earth  than  at 
the  equator,  it  follows  that  a  given  mass  at  or  near  the  poles 
will  weigh  more  than  at  or  near  the  equator. 

2.  Weight  above  or  below  the  surface.     The  weight  of  a 
body  above  or  below  the  surface  is  less  than  at  the  surface. 


40  HIGH   SCHOOL  PHYSICS 

A  mass  weighing  100  pounds,  for  example,  at  the  surface  of 
the  earth  will  weigh  less  than  100  pounds  if  taken  up  in  a 
balloon  or  down  into  a  mine.  (Supplement,  545.) 

67.  Centrifugal  Force  and  Weight.     There  are  two  reasons 
why  a  given  body  weighs  less  at  the  equator  than  at  the  poles. 
The  first  is  because  the  force  of  gravity,  as  has  already  been 
explained,  is  less  at  the  equator  than  at  the  poles;    and  the 
second  is,  that  the  centrifugal  force  is  greater  at  the  equator 
than  at  the  poles.     For  the  last  named  reason  the  tendency  of 
all  bodies  at  the  equator  to  fly  off  into  space  is  greater  than  at 
or  near  the  poles.     Bodies  at  the  equator  have  a  velocity, 
due  to  the  rotation  of  the  earth,  of  more  than  1000  miles  per 
hour.     The  resulting  centrifugal  force  is  about  -j|-^  of  the  force 
of  gravity.     Now,  since  centrifugal  force  is  proportional  to  the 
square  of  the  velocity,  and  the  square  of  17  is  289,  it  follows 
that  if  the  earth  should  rotate  17  times  as  fast  as  it  now  does, 
bodies  at  the  equator  would  weigh  nothing;    and  should  the 
rate  of  rotation  increase  beyond  this  point,  they  would  fly  off 
into  space. 

68.  Center  of  Gravity.     The  center  of  gravity  of  a  body  is 
the  point  of  application  of  the  resultant  of  all  the  forces  of  gravity 
acting  upon  it.     It  is  a  point  about  which  the  body  may  be 
balanced.     If  a  meter  stick,  for  example,  be  balanced  upon  the 
finger,  the  center  of  gravity  of  the  stick  lies  in  the  body  directly 
above  the  point  of  support. 

The  center  of  gravity  of  a  regular  homogeneous  body  is  at  its 
geometrical  center.  The  center  of  gravity  of  a  cube  lies  at  the 
point  of  intersection  of  its  diagonals;  that  of  a  circular  disc 
at  its  center  of  figure. 

The  center  of  gravity  of  an  irregular  body,  as  for  example  a 
chair,  Fig.  31,  may  be  determined  by  suspending  it  succes- 
sively from  two  different  points  and  noting  the  intersection  of 
the  direction  of  the  plumb  line.  If  a  piece  of  metal,  such 
as  iron  or  lead,  be  suspended  by  means  of  a  string,  Fig.  32, 
the  device  is  known  as  a  plumb  line;  that  is,  a  line  deter- 


MECHANICS   OF   SOLIDS 


41 


mining  a  vertical  direction;  the  piece  of  metal  is  called 
the  "  bob."  Experiment.  Suspend  from  two  points  E  and 
C  an  irregular  shaped  piece  of  board,  Fig.  33,  and  note 


Fia.  31 


FIG.  32 


the    point    of    intersection    of    the    plumb    lines    E   and   C. 
The  center  of  gravity  of  the  board  lies  on  a  line  passing 


FIG.  33 


FIG.  34 


through  the  intersection  of  lines  E  and  C,  midway  between 
the  faces.  In  a  similar  manner  it  may  be  shown  that  the 
center  of  gravity  of  a  triangular  piece  of  board  lies  at  the 
intersection  of  its  median  lines,  Fig.  34.  The  center  of 


42 


HIGH  SCHOOL  PHYSICS 


gravity  of  a  body  may  lie  entirely  outside  the  material  of 
the  body,  as  in  the  case  of  a  ring  or  of  a  lamp  chimney. 

Center  of  gravity  is 
sometimes  called  center 
of  mass. 

69.  Line  of  Direction. 
The  line  of  direction  is 
a  straight  line  passing 
through  the  center  of 
gravity  of  a  body  and 
the  center  of  the  earth. 


FIG.  35 


FIG.  36 


Whether  a  body  stand 
or    fall    depends    upon 

the  position  of  its  line  of  direction  with  respect  to  its  base. 

If  this  line  fall  within  the  base, 

Fig.  35,  the  body  will  stand;  if 

it  fall  without  the  base,  Fig.  36, 

the  body  will  fall.     There  are 

in  Europe  a  number  of  "  lean- 
ing towers  "  which  illustrate  in 

a  very  striking  manner  the  rela- 
tion of  the  stability  of  a  body 

to   the   position   of   its   line   of 

direction.      Among    the    most 

noteworthy    structures   of    this 

type  are  the  leaning  towers  of 

Bologna,  Fig.  37.     The  taller  of 

these  two  towers  is  320  feet  in 

height  and  leans  out  of  plumb 

4  feet;  that  is,  the  middle   of 

the  tower  leans  4  feet  from  a 

plumb  line  dropped  through  the 

middle  of  the  base.     The  shorter 

tower  is  163  feet  in  height  and 

is  out  of  plumb  by  10  feet.     One  of  the  most  famous  leaning 


FIG.  37 
Leaning  Towers  of  Bologna 


MECHANICS  OF   SOLIDS 


43 


FIG.  38 


towers  is  that  of  the  bell  tower  of  the  Cathedral  of  Pisa. 
This  tower  is  179  feet  in  height  and  its  top  leans  from  the 
vertical,  as  computed  in  1910,  a  distance  of  16.5  feet. 

70.  Three  States  of  Equilibrium.  The  three  states  of  equi- 
librium which  a  body  may  possess  are  stable,  unstable,  and 
neutral,  illustrated  by 
a  cone  as  shown  in 
Fig.  38.  A  body  is 
said  to  be  in  stable 
equilibrium  if  a  turn- 
ing motion  about  any 
point  in  its  base,  such 
as  would  occur  in  tip- 
ping it  over,  tends  to  raise  its  center  of  gravity.  A  book  lying 
on  the  table  is  in  stable  equilibrium  because  its  center  of  grav- 
ity rises  if  it  be  turned  upon  its  edge.  A  cone  resting  upon  its 
base,  A  of  Fig.  38,  is  a  good  illustration  of  stable  equilibrium. 
A  body  is  in  unstable  equilibrium  if  a  turning  motion  tends  to 
lower  its  center  of  gravity.  A  cone  resting  upon  its  ^vertex 
is  in  unstable  equilibrium  because  any  turning  motion  about  the 
point  of  support  will  cause  its  center  of  gravity  to  be  lowered. 
A  body  is  in  neutral  equilibrium  if  a  turning  motion  neither 
raises  nor  lowers  its  center  of  gravity,  as  in  the  case  of  the  cone 

lying  on  its  side.  A 
spherical  ball  is  also 
an  excellent  illustra- 
tion of  neutral  equi- 
librium. 

71.  Stability  of  a 
Body.  The  stability 
of  a  body  is  deter- 


b 
a 

B 

c  ?"-~:: 

b 
a 

C 

A     c/              - 

FIG.  39 


mined  by  the  amount  of  work  required  to  overturn  it;  that  is, 
the  amount  of  work  necessary  to  lift  the  center  of  mass  of  the 
body  through  a  vertical  distance  ab,  Fig.  39.  There  are  two 
ways  by  which  the  stability  of  a  body  may  be  increased;  namely, 


44  HIGH  SCHOOL  PHYSICS 

(a)  by  broadening  the  base,  (b)  by  lowering  the  center  of  grav- 
ity. In  A,  B,  and  C  of  Fig.  39  we  have  three  bodies  of  the 
same  shape  and  size.  In  C  the  center  of  gravity  is  lower  than 
in  A  and  B,  due  to  the  loading  of  one  end  of  the  vessel  with  some 
heavy  material. 

EXERCISES.    2.  Explain,  (a)  why  A  is  more  stable  than  B;    (b)  why  C 
is  more  stable  than  B. 

3.  Which  is  the  more  stable,  a  load  of  hay  or  a  load  of  coal,  each  weigh- 
ing the  same?     Why? 

4.  Why  does  a  person  in  carrying  a  heavy  pail  of  water  throw  out  the 
opposite  arm,  as  shown  in  Fig.  40? 


FIG.  40  FIG.  41 

6.  Two  table  forks  may  be  balanced  on  the  edge  of  a  tumbler  by  means 
of  a  coin,  or  better  still,  a  strong  toothpick,  as  shown  in  Fig.  41.  Explain. 

6.  A  person  standing  with  his  heels  and  back  against  a  wall  cannot 
pick  up  anything  from  the  floor  in  front  of  him  without  falling.  Why? 

THE  PENDULUM 

72.  Definition  of  Terms.  A  pendulum  is  a  body  suspended 
so  that  it  may  vibrate  freely.  Experiment.  Let  an  iron  ball 
attached  to  a  string  be  suspended  as  shown  in  Fig.  42.  This 
constitutes  a  pendulum.  When  it  is  at  rest  it  lies  in  a  vertical 
position  PO.  If  drawn  aside  to  some  point,  as  A,  and  liberated 
it  will  oscillate  back  and  forth,  each  swing  being  somewhat 
shorter  than  the  preceding  one,  until  it  finally  comes  to  rest. 


MECHANICS   OF   SOLIDS 


45 


A  complete  vibration  is  a  swing  from  one  side  to  the  other 
and  back  again;  that  is,  from  A  to  B  and  back  to  A  again. 
A  simple  vibration  is  a  swing  from  one  side  of  the  arc  to  the 
other;  that  is,  from  A  to  B.  The  amplitude 
is  one-half  the  arc  described  in  a  single  swing. 

The  period,  or  time  of  vibration,  is  the  time 
required  to  make  one  vibration.  The  period 
of  a  complete  vibration  is  twice  that  of  a 
simple  vibration.  It  is  important  to  note 
that  the  term  period  refers  to  the  time  re- 
quired to  make  one  vibration  (simple  or  com- 
plete), and  has  no  reference  to  the  time 
required  for  the  pendulum  to  come  to  rest. 

73.    The  Relation  of  the  Period  to  the  Num- 
ber  of  Vibrations.     If  a  pendulum  make  20 
vibrations  in  10  seconds,  the  number  of  vibra- 
tions per  second  will  be  n  =  fir  =  2.     Also,  its  period  will  be 
T  =  iir  =  T-     Hence  it  appears  that  the  period  of  a  pendulum 
is  equal  to  the  reciprocal  of  the  number  of 

vibrations  per  second;  that  is,  T  =  — 

TT' 

74.    Motion  of   the    Pendulum  Explained. 
Consider  the  pendulum,  Fig.  43,  to  be  drawn 
aside  to  the  point  A.     It  is  acted  upon  by 
the  force  of  gravity,  represented  by  the  line 
j     AG.     This  force  may  be  resolved  into  two 
I    components;  one,  AC,  producing  a  tension  in 
Q  the  string,   and  the  other,  AB,  tending  to 
produce  motion  toward  0.     The  pendulum, 
then,  tends  to  move  from  A  to  0  due  to  a 
component  of  the  force  of  gravity.     It  con- 
tinues to  swing  beyond  0  due  to  its  inertia. 
If  there  were  no  friction   to   interfere,  the 
pendulum  would  rise  as  high  on  one  side  of  the  arc  as  on  the 
other;   that  is  to  say,  it  would  never  come  to  rest. 


46  HIGH  SCHOOL  PHYSICS 

75.  Simple  and  Compound  Pendulums.  A  simple  pendulum 
may  be  defined  as  a  material  point  suspended  by  a  weightless 
thread.  An  actual  simple  pendulum  does  not,  of  course,  exist, 
since  any  thread,  however  small,  must  have  some  weight.  A 
small  lead  bullet,  however,  suspended  by  a  fine  thread  may  be 
considered  as  an  illustration  of  a  simple  pendulum.  A  com- 
pound pendulum  is  any  body  suspended  so  as  to  vibrate  freely. 
A  meter  stick  vibrating  about  one  end  is  a  compound  pendulum. 
Q^  -__  In  fact  all  pendulums  in  actual  use  are  compound 

pendulums,  differing  only  in  their  approximation  to 
the  ideal  simple  type.  The  pendulum  of  a  clock, 
for  instance,  is  a  compound  pendulum  in  which 
most  of  the  mass  is  in  the  bob. 

76.  Relation  of  the  Period  of  a  Pendulum  to 
its  Length.  Experiment.  This  relation  may  be 
demonstrated  experimentally  as  follows:  Suspend 
two  pendulums  A  and  B,  Fig.  44,  having  lengths 
of  1  meter  and  \  meter  respectively.  Determine 
the  period  in  each  case  by  allowing  each  pendu- 
lum to  vibrate  for  one  minute.  Pendulum  A  will 
make  60  vibrations  (very  nearly)  in  60  seconds;  and 
J5,  120  vibrations  in  the  same  time.  The  period  of 
A  is,  therefore,  f$  =  1;  the  period  of  B,  T6A  =  \. 

Thus  it  appears  (a)  that  the  longer  pendulum 
-p  ..  has  the  greater  period;  that  is,  the  longer  the  pen- 
dulum the  slower  it  goes;  and  (b)  the  period  of 
vibration  is  directly  proportional  to  the  square  root  of  the 
length;  that  is,  T'T'  =  vT  V77 

EXERCISES.  7.  If  we  consider  that  a  pendulum  1  meter  in  length  has 
a  period  of  1  second,  what  will  be  the  period  of  a  pendulum  (a)  i  of  a  meter 
in  length?  (b)  4  meters  in  length? 

8.  How  many  vibrations  will  each  of  the  three  pendulums  of  exercise  7 
make  in  1  minute? 

9.  What  will  be  the  relative  periods  of  two  pendulums  whose  lengths 
are  4  ft.  and  9  ft.  respectively? 


MECHANICS   OF   SOLIDS  47 

77.  Relation  of  Period  to  Acceleration.     Experiment.     Set 
in  vibration  two  pendulums,  A  and  B,  of  the  same  length  and 
having  iron  bobs.     Under  A  place  the  pole  of  a  strong  magnet. 
Pendulum  B  will  vibrate  due  to  the  force  of  gravity  alone;  the 
vibrations  of  A,  on  the  other  hand,  will  be  due  to  both  the  force 
of  gravity  and  the  force  exerted1  by  the  magnet.     Pendulum 
A  will  vibrate  faster  than  B;  hence  its  period  will  be  shorter. 

According  to  this  experiment,  the  greater  the  force  acting  upon 
a  pendulum  (and  hence  the  greater  the  acceleration)  the  faster  it 
goes. 

It  has  been  shown  experimentally  that  the  period  of  a 
pendulum  is  inversely  proportional  to  the  square  root  of  the 
acceleration  of  gravity;  that  is, 

T:  T'  =  vT":  V~g 

EXERCISES.  10.  How  would  the  period  of  a  pendulum  at  the  poles  of 
the  earth  compare  with  its  period  at  the  equator?  Why? 

11.  Two  pendulums,  one  at  the  base  of  a  mountain  and  the  other  at 
the  top,  are  to  make  the  same  number  of  vibrations  per  minute.     Which 
must  be  the  longer,  and  why? 

12.  If  the  acceleration  of  gravity  were  increased  fourfold,  how  would 
the  period  of  a  given  pendulum  be  affected,  and  how  much? 

78.  Relation  of  Period  to  Length  of  Arc.     Experiment.     If 
a  pendulum  of  given  length,  1  meter  for  example,  be  allowed  to 
vibrate  through  an  arc  of  several  degrees,  the  number  of  vibra- 
tions be  counted  for  one  minute,  the  pendulum  then  be  allowed 
to  vibrate  through  a  very  much  smaller  arc,  and  the  number 
of  vibrations  be  again  counted  for  a  minute,  it  will  be  found  that 
the  period  in  each  case  is  practically  the  same.     That  is  to 
say,  the  period  of  vibration  is  independent  of  the  length  of  the  arc, 
Fig.  45.     This  fact    was  first  discovered  by  Galileo  (1566- 
1642),  who  observed  that  the  vibrations  of  a  swinging  lamp 
in  the  Cathedral  of  Pisa,  as  timed  by  his  own  pulse,  occurred 
in  equal  intervals,  whether  the  amplitude  was  large  or  small. 
This  discovery  led  to  the  use  of  the  pendulum  as  an  instru- 
ment for  the  measurement  of  time  in  clocks. 


48 


HIGH   SCHOOL   PHYSICS 


FIG.  45 


It  must  be  noted  in  this  connection,  however,   that  the 
period  of  a  pendulum  is  independent  of  the  arc  only  when  the 
arc  is  relatively  small;  indeed,  the  law  holds  strictly  when 
_  _        the    amplitude    of   vibration  is  not 

much    greater    than    three    degrees. 
(Supplement,  546.) 

79.  Relation  of  Period  to  Mass. 
Experiment.  Suspend  two  pendu- 
lums having  the  same  length,  the 
bob  of  one  being  of  iron  and  that 
of  the  other  of  some  light  material 
such  as  cork  or  wood,  Fig.  46.  Let 
each  vibrate  for  the  same  time,  half 
a  minute  say,  and  count  the  number 

of  vibrations.     It  will  be  observed  that  while  the  pendulum 
having  the  greater   mass   tends   to    continue  in  motion   for 
a   greater   length   of    time   than   the   lighter    one,   yet    both 
make  the  same  number  of  vibrations  per  unit  of 
time.     The  period  of  vibration  is  independent  of  the 
mass  of  the  bob.     It  is  important  to  note  that  this 
law  does  not  hold  when  the  vibrations  are  forced. 
By  a  forced  vibration  of  a  pendulum  we  mean  one 
which  is  due  to  some  other  force  than  gravity,  as, 
for  example,  the  vibration  of  a  pendulum  of  a  clock, 
which  is  due  to  the  force  of  the  spring  or  weight. 
If  the  bob  be  removed  from  the  pendulum  of  a  clock, 
thus  diminishing  the  mass,  the  rate  of  vibration  will 
be  much  increased. 

80.  Laws  of  the  Pendulum.  The  main  facts  illus- 
trated by  the  preceding  experiments  may  be  ex- 
pressed in  the  following  laws  for  the  simple  pendulum  : 

I.  The  period  of  vibration  of  a  pendulum  is  directly  propor- 
tional to  the  square  root  of  its  length. 

II.  The  period  of  vibration  is  inversely  proportional   to   the 
square  root  of  the  acceleration  of  gravity. 


FIG.  46 


MECHANICS   OF   SOLIDS 


49 


III.  The  period  of  vibration  is  independent  of  the  amplitude, 
provided  the  amplitude  be  small. 

IV.  The  period  of  vibration  is  independent  of  the  mass. 
These  laws  of  the  pendulum  may  be  combined  into  a  single 

equation, 


in  which  T  is  the  period,  in  seconds,  of  a  simple  vibration;  I  is 
the  length  of  the  equivalent  simple  pendulum  in  feet  or  centi- 
meters; g  is  the  acceleration  of  gravity  in  feet  (32),  or  in  centi- 
meters (980),  per  second  per  second.  The  constant  TT  (3.1416) 
occurs  here,  as  in  a  great  many  mathematical  equations,  because 
the  equation  involves  the  ratio  of  the  circum- 
ference of  a  circle  to  its  radius. 

EXERCISE.  13.  Find  the  period  of  a  simple  vibra- 
tion of  a  pendulum  108.9  cm.  in  length  at  Washington, 
D.  C.,  g  being  980.1. 


81.  Use  of  the  Pendulum  in  Measuring 
Time.  The  most  common  use  of  the  pendu- 
lum is  in  the  measurement  of  time.  Since  its 
vibrations  are  performed  in  equal  intervals  of 
time,  that  is,  they  are  isochronous,  all  that  is 
needed  is  some  mechanical  device  to  keep  the 
pendulum  vibrating  and  to  enable  it  to  regu- 
late the  motion  of  the  hands.  The  motive 
power  of  the  clock  is  supplied  by  weights  or 
springs;  the  motion  of  the  hands  is  regulated 
by  means  of  an  escapement,  Fig.  47.  As  the 
pendulum  swings  to  and  fro  the  projections  of 
the  escapement  catch  alternately  in  the  teeth 
of  the  escapement  wheel,  thus  allowing  only 
one  tooth  to  escape  for  each  double  swing. 
If  the  escapement  wheel,  therefore,  has  30  teeth,  it  will  rotate 
once  while  the  pendulum  makes  30  complete  vibrations. 


FIG.  47 


50  HIGH   SCHOOL   PHYSICS 

In  order  that  the  periods  may  be  equal,  the  length  of  the 
pendulum  must  always  be  the  same.  In  summer  the  pendu- 
lum, however,  lengthens,  hence  the  clock  tends  to  lose  time;  in 
winter  the  pendulum  shortens  and  the  clock  gains  time.  Cor- 
rections must  therefore  be  made  for  changes  in  length  due  to 
changes  in  temperature.  This  may  be  done  by  moving  the 
bob  up  or  down  by  means  of  a  nut  or  thumb  screw.  Changes 
in  the  length  of  a  pendulum  due  to  changes  of  temperature  may 
also  be  automatically  corrected  by  means  of  compensating 
devices.  A  compensation  pendulum  is  one  that  is  made  of 
two  or  more  metals  so  regulated  as  to  expand  in  opposite  direc- 
tions (Art.  204),  and  thereby  keep  the  length  of  the  pendulum 
constant. 

82.  Use  of  the  Pendulum  in  Determining  g.     If  the  period 
of  a  pendulum  of  given  length  be  determined  by  experiment, 
the  value  of  the  acceleration  g  due  to  gravity  at  any  place  may 
be  determined  by  means  of  the  equation 

T  = 

The  value  of  g  has  thus  been  determined  for  a  great  many 
places.  For  example,  at  Boston  g  =  980.38;  Chicago,  980.26; 
Denver,  979.6. 

EXERCISE.  14.  The  period  of  a  pendulum  1  meter  in  length  at  Pike's 
Peak,  Col.,  is  1.004  seconds.  Find  the  value  of  g. 

83.  Center  of   Oscillation.     Experiment.     Suspend  side  by 
side  a  meter  stick  and  a  pendulum  consisting  of  a  lead  bullet 
attached  to  a  fine  thread,  Fig.  48.     Set  the  two  pendulums 
vibrating  and  then  shorten  the  simple  pendulum  until  the  two 
vibrate  in  the  same  time.     The  meter  stick  represents  a  com- 
pound pendulum;   the  bullet  and  thread,  a  simple  pendulum. 
The  length  of  the  meter  stick,  considered  as  a  pendulum,  is  the  dis- 
tance from  the  point  of  suspension  S  to  the  point  0,  which  corre- 
sponds to  the  position  of  the  bob  of  the  simple  pendulum.     The 


MECHANICS   OF   SOLIDS 


51 


point  0  is  called  the  center  of  oscillation  of  the  compound  pendu- 
lum. When  we  speak  of 'the  length  of  a  compound  pendulum 
we  mean  a  length  that  is  equivalent  to  a  simple  pendulum 
having  the  same  period.  Thus  the  length  of  the  meter  stick, 
considered  as  a  pendulum,  is  the  distance  I  measured  from  the 
point  of  suspension  S  to  the  point  0. 

If  the  compound  pendulum  be  a  thin  uniform  rod,  as  in  the 
case  of  the  meter  stick,  its  length  I,  if  suspended  from  the 
end,  is  two-thirds  of  its  entire  length.  If  it  is  not  uniform, 
however,  as  in  the  case  of  a  ball  bat,  the  length  I  has  to  be 
determined  by  experiment. 

EXERCISE.  16.  What  is  the  period  of  vibration  of  a  uniform  thin  rod 
12  ft.  in  length,  the  value  of  g  being  32  ft.  per  second  per  second? 


FIG.  48 


FIG.  49 


84.  Center  of  Percussion.  Experiment.  Suspend  a  rod  by 
means  of  a  string  held  in  one  hand,  Fig.  49.  (a)  Strike  the 
rod  near  its  upper  extremity.  This  end  moves  in  the  direction 
of  the  blow,  and  at  the  same  time  a  sudden  jerk  is  felt  by  the 
hand,  (b)  Again,  strike  the  rod  in  the  same  direction  near  its 
lower  extremity.  The  upper  end  moves  in  a  direction  opposite 


52  HIGH  SCHOOL  PHYSICS 

to  the  stroke  and  a  jerk  is  again  felt  by  the  hand,  (c)  Now 
strike  the  rod  in  the  neighborhood  of  its  center  of  oscillation. 
Both  ends  of  the  stick  move  forward  together,  and  no  jerk  is 
felt  by  the  hand.  This  point  is  called  the  center  of  percussion. 
In  a  compound  pendulum  the  center  of  percussion  is  a  point  coinci- 
dent with  the  center  of  oscillation.  In  the  case  of  the  experiment 
above,  we  must  consider  the  hand  as  the  point  of  suspension 
of  the  pendulum.  The  center  of  percussion  is  a  point  where  a 
blow,  given  or  received,  is  most  effective  and  produces  the  least 
strain  on  the  support  or  axis  of  motion.  The  baseball  player 
soon  learns  at  what  point  on  the  bat  he  can  deal  the  most  effec- 
tive blow  and  at  the  same  time  produce  the  least  tingle  in  his 
hand. 

WORK,  POWER,  ENERGY 

85.  Work.     Work   is   the   overcoming   of  resistance   through 
space.     As  used  in  physics,  the  term  work  involves  two  ideas, 
force  and  space.     If  a  man  were  to  hold  up  a  heavy  weight 
without  giving  it  motion,  he  would  not  be  doing  work  in  the 
physical  sense.     The  moment  he  moves  the  body,  that  is, 
applies  force  through  space,  he  does  work. 

86.  Work  Does  not  Involve  the  Factor  of  Time.     If  a  weight 
be  lifted  from  the  floor  to  the  table  in  10  seconds,  a  given 
amount  of  work  is  done.     Again,  if  the  same  weight  be  lifted 
through  the  same  space  in  10  minutes,  or  in  10  hours,  the  same 
amount  of  work  is  done  as  in  the  first  case.     A  train  of  cars 
hauled  from  one  station  to  another  requires  a  given  amount  of 
work,  no  matter  what  the  time  involved.     Likewise,  the  work 
done  by  the  carpenter  in  sawing  a  board  is  measured  only 
by  the  resistance  overcome  and  the  space  through  which  the 
saw  cuts. 

Work  =  force  X  space 
w  =  Fs 

87.  Units  of  Work.     Since  work  is  force  times  space,  the 
units  in  which  work  is  measured  depend  upon  the  units  chosen 


MECHANICS  OF  SOLIDS  53 

for  force  and  space.     There  are,  therefore,  for  work,  as  in  the 
case  of  force,  two  sets  of  units,  the  gravitational  and  absolute. 

7 1  foot  pound 
gravitational  \ 

qram  centimeter 
Units  of  work  I 

absolute 

(erg 

The  foot  pound  is  the  work  done  by  a  force  of  one  pound  acting 
through  a  space  of  one  foot.  The  gram  centimeter  is  the  work 
done  by  a  force  of  one  gram  acting  through  a  space  of  one  centi- 
meter. The  kilogram  meter  is  sometimes  used  instead  of  the 
smaller  unit,  the  gram  centimeter.  A  kilogram  meter  is  the 
work  done  by  a  force  of  one  kilogram  acting  through  a  space 
of  one  meter. 

The  foot  poundal  is  the  work  done  by  a  force  of  one  poundal 
acting  through  a  space  of  one  foot.  The  erg  is  the  work  done  by 
a  force  of  one  dyne  acting  through  a  space  of  one  centimeter. 

The  two  units  of  work  ordinarily  employed  are  the  foot 
pound  and  the  erg.  Since  the  erg  is  a  very  small  quantity, 
a  larger  unit  called  the  joule  is  sometimes  used.  A  joule  is 
ten  million  (10,000,000)  ergs.  The  relation  of  gravitational  to 
absolute  units  of  work  is  expressed  as  follows:  1  foot  pound 
=  32  foot  poundals;  1  gram  centimeter  =  980  ergs. 

EXERCISES.  16.  A  weight  of  10  Ibs.  is  lifted  vertically  to  a  height 
of  10  ft.  Find  the  work  done  in  (a)  gravitational  units;  (b)  absolute 
units. 

17.  A  force  ca  10  grams  acts  through  a  space  of  10  cm.     Find  the  work 
done  in  (a)  gravitational  units;  (b)  absolute  units. 

18.  A  hqpse  pulling  a  load  of  1  ton  along  a  smooth  road  exerts  a  force 
of  500  Ibs.  *  How  much  work  in  foot  pounds  is  done  by  the  horse  if  the 
load  be  hauled  a  distance  of  1  mile? 

88.  Power.  Power  is  the  time  rate  of  doing  work.  It  is 
work  divided  by  time;  that  is, 

work      w 
power  =  - — 

time        t 


54  HIGH   SCHOOL  PHYSICS 

89.  Units  of  Power.  The  English  unit  is  the  horse  power 
(H.P.);  the  metric  unit  is  the  watt,  named  after  James  Watt, 
the  inventor  of  the  steam  engine. 

A  horse  power  is  the  expenditure  of  33,000  foot  pounds  of  work 
per  minute,  or  550  foot  pounds  per  second.  A  watt  is  equal  to 
10,000,000  ergs  per  second;  that  is,  1  joule  per  second.  A  kilowatt 
(K.W.)  =  1000  watts.  One  H.P.  =  f  K.W.  (very  nearly). 

foot  pounds  foot  pounds 


H.P.  = 
watts  = 


33,000  X  time  in  minutes      550  X  seconds 

ergs 
10,000,000  X  time  in  seconds 


When  the  horse  power  was  first  proposed  as  the  unit  of  power 
it  was  thought  that  a  strong  horse  was  capable  of  doing  about 
33,000  foot  pounds  per  minute.  It  has  since  been  determined 
that  the  power  of  an  ordinary  horse  for  continuous  work  is 
considerably  below  this  value.  In  fact  the  average  horse  has 
a  power  of  f  H.P. ;  that  of  an  ordinary  man  about  f  H.P.  The 
power  of  the  railroad  locomotive  varies  from  500  to  2000  H.P.; 
that  of  the  engines  of  our  large  ocean  liners  from  10,000  to 
40,000  H.P.  It  is  important  to  note  that  while  the  power  of 
an  average  man  is,  for  continuous  work,  far  below  that  of  a 
horse,  yet  for  a  short  time  the  man  may  work  at  a  rate  greater 
than  that  of  a  horse  power.  A  person  in  running  upstairs,  for 
instance,  works  at  a  rate  considerably  above  a  horse  power. 

EXERCISES.  19.  During  the  construction  of  a  building  4950  Ibs.  of 
brick  were  elevated  to  a  height  of  20  ft.  in  10  minutes.  At  what  rate, 
in  H.P.,  was  the  work  done? 

20.  A  500  kilogram  weight  was  lifted  to  a  vertical  height  of  10  meters 
in  10  seconds.     At  what  rate  was  the  work  done  in  (a)  gram  centimeters 
per  second?    (b)  ergs  per  second?   (c)  watts? 

21.  How  many  gallons  of  water  can  an  8  horse  power  engine  throw  to 
a  height  of  30  ft.  in  a 'quarter  of  an  hour,  assuming  that  a  gallon  of  water 
weighs  8  Ibs.? 

22.  An  engine  lifts  198  tons  of  ore  per  hour  from  a  mine  1000  ft.  deep. 
Find  the  power  of  the  engine  in  (a)  H.P.;    (b)  kilowatts. 


MECHANICS  OF  SOLIDS  55 

90.  Energy.     Energy  is  the  capacity  that  a  body  has  for  doing 
work.     The  steam  in  an  engine  possesses  energy  because  in 
expanding  it  is  capable  of  doing  work.     The  water  in  a  mill 
dam,  the  coiled  spring  of  a  watch,  the  muscles  of  the  body,  all 
possess  energy  because  they  have  the  capacity  for  doing  work. 

The  units  in  which  energy  is  measured  are  the  same  as  the  units 
of  work ;  namely,  the  foot  pound,  foot  poundal,  gram  centimeter, 
and  the  erg. 

Energy  is  of  two  kinds,  potential  and  kinetic. 

91.  Potential  Energy.     Potential  energy  is  the  energy  which  a 
body  possesses  by  virtue  of  its  position,  or  by  virtue  of  its  tendency 
to  change  chemically.     A  body  lifted  from  the  floor  to  the  table 
possesses  energy  by  virtue  of  its  position,  because  if  it  were 
allowed  to  fall  from  the  table  to  the  floor  it  would  do  work.     A 
lump  of  coal  possesses  potential  energy  because  of  its  affinity  for 
oxygen,  that  is,  its^  tendency  to  burn.     Gunpowder,  likewise, 
possesses  potential  energy  because  of  its  tendency  to  explode. 

The  potential  energy  of  a  body  due  to  its  position  may  be 
measured  by  the  work  required  to  put  it  in  place.  For  example, 
a  body  lies  upon  the  table.  Its  potential  energy  with  respect 
to  the  floor  is  equal  •  to  the  work  required  to  lift  it  from  the 
floor  to  the  table. 

Potential  energy  =  work  =  force  X  space 
p.E.  =  w  =  Fs 

EXERCISES.  23.  A  piece  of  metal  weighing  10  Ibs.  is  lifted  from  the 
floor  to  the  table,  a  distance  of  3  ft.  Find  its  potential  energy  in  foot 
pounds. 

24.  A  mass  of  20  grams  rests  on  a  shelf  3  meters  above  the  floor.     What 
is  its  potential  energy  with  respect  to  the  floor  in  (a)  gram  centimeters? 
(b)  ergs? 

25.  A  mass  of  1  kilogram  is  lifted  to  a  height  of  2  meters.     Find  its 
potential  energy  in  (a)  kilogram  meters;  (b)  gram  centimeters;  (c)  ergs. 

92.  Kinetic  Energy.     Kinetic  energy  is  the  energy  which  a 
body  possesses  by  virtue  of  its  motion.     We  instinctively  avoid 
bodies  that  are  in  rapid  motion.     Experience  has  taught  us  that 


56  HIGH  SCHOOL  PHYSICS 

such  bodies  possess  energy  —  the  greater  the  motion  the  greater 
the  energy.  Let  us  consider  the  case  of  the  bullet  and  the 
gun.  We  have  learned  from  the  third  law  of  motion  that  the 
momenta  of  the  two  are  equal.  This  does  not  imply,  however, 
that  their  energies  are  equal.  The  energy  of  the  bullet  is  enor- 
mously greater  than  that  of  the  gun  because  of  its  greater 
velocity.  The  kinetic  energy  of  a  body  varies  directly  as  its 
mass  and  the  square  of  its  velocity.  If  the  velocity  of  a  body 
be  doubled  its  energy  is  increased  fourfold;  if  the  velocity  be 
trebled  its  energy  is  increased  ninefold,  and  so  on. 

Experiment.  If  a  bullet  be  dropped  from  a  height  of  2  feet 
into  a  pail  of  soft  clay  it  will  penetrate  to  a  certain  depth, 
depending  on  the  softness  of  the  clay.  If  now  the  bullet  be 
dropped  from  a  height  of  8  feet,  such  that  its  velocity  on 
striking  the  clay  is  twice  as  great  as  in  the  first  instance,  it  will 
penetrate  to  nearly  4  times  the  depth  that  it  did  in  the  former 
case.  It  can  be  shown  (Supplement,  547)  that  the  following 
equation  for  kinetic  energy  holds: 

K.E.  =  \rntf 

in  which  m  is  the  mass  of  the  body  and  v  its  velocity.  This 
equation  expresses  the  kinetic  energy  in  absolute  units  (foot 
poundals  or  ergs). 

Example.  A  body  having  a  mass  of  16  pounds  moves  with 
a  velocity  of  20  feet  per  second.  Find  its  K.E.  Solution : 
K.E.  =  \rntf  =  |  X  16  X  400  =  3200  foot  poundals  =  100  foot 
pounds. 

EXERCISES.  26.  A  mass  of  64  Ibs.  is  moving  with  a  velocity  of  10 
ft.  per  second.  Find  its  K.E.  in  (a)  absolute  units  (foot  poundals); 
(b)  gravitational  units  (foot  pounds). 

27.  A  mass  of  196  g.,  moving  with  a  velocity  of  10  cm.  per  second,  has 
what  K.E.  in  (a)  ergs?  (b)  gram  centimeters? 

93.  Transformation  of  Energy.  Potential  energy  and  ki- 
netic energy  are  so  related  that  when  one  disappears  the  other 
appears.  If  a  stone  be  thrown  upward  it  has  its  maximum 


MECHANICS  OF  SOLIDS  57 

kinetic  energy  at  the  instant  it  leaves  the  hand,  because  its 
velocity  at  this  instant  is  greatest.  As  it  rises  its  kinetic  energy 
decreases  and  its  potential  energy  increases.  When  it  reaches 
its  highest  point  its  potential  energy  is  a  maximum;  its  kinetic 
energy,  zero.  Thus,  in  ascending  there  is  a  transformation 
from  kinetic  to  potential  energy;  in  descending  a  reverse  trans- 
formation occurs;  that  is,  the  potential  energy  again  becomes 
kinetic  energy,  reaching  a  maximum  when  the  velocity  is  the 
greatest. 

94.  The  Conservation  of  Energy.     The  law  of  the  conser- 
vation of  energy  states  that  the  energy  in  the  universe  is  con- 
stant in  quantity;   it  cannot  be  created  or  destroyed.     When 
work  is  done,  one  body  loses  energy  and  another  gains  it.     The 
doing  of  work,  therefore,  involves  a  transference,  and  often  a 
transformation  as  well,  of  energy.     The  potential  energy  pos- 
sessed by  a  lump  of  coal  is  transformed  into  heat  energy  in 
the  furnace,  then  to  the  steam  in  the  engine,  thence  to  the 
motion  of  the  wheels,  and  so  on.     No  energy  is  destroyed;  it  is 
only  transformed  from  one  form  to  another. 

MACHINES 

95.  Definitions.     A  machine  is  a  device  for  transferring  or 
transforming  energy".     A  steam  engine,  together  with  the  boiler, 
is  a  machine  for  transforming  the  potential  energy  of  coal  into 
the  kinetic  energy  of  mechanical  motion.     A  dynamo  is  a 
machine  which  may  be  used  for  transforming  the  energy  of 
mechanical  motion  into  the  energy  of  an  electric  current.     A 
hammer,  a  pair  of  scissors,  a  jack  knife,  a  pencil  are  all  types 
of  machines  for  transferring  energy  from  one  point  to  another. 

96.  Friction.     Whenever  one  body  slides  or  rolls  over  an- 
other, friction  is  encountered.    A  part  of  the  energy  applied  to 
any  mechanical  device  is,  therefore,  expended  in  overcoming 
friction,  which  manifests  itself  as  a  resistance  offered  to  the 
motion  of  one  body  upon  another. 


58 


HIGH  SCHOOL  PHYSICS 


The  following  facts  concerning  friction  have  been  estab- 
lished by  experiment:  (a)  Friction  depends  upon  the  nature  of 
the  substance  and  the  condition  of  the  surfaces,  but  is  independent 
of  the  area  of  the  surfaces  in  contact.  Experiment.  Attach  a 
spring  balance  to  a  brick,  the  broad  surface  of  which  is  in 
contact  with  the  table,  as  shown  in  Fig.  50.  By  means  of  the 


FIG.  50 


spring  balance,  draw  the  brick  over  the  surface  of  the  table 
with  a  uniform  motion  and  note  the  reading  of  the  balance. 
Now  place  the  brick  with  its  narrow  face  in  contact  with  the 
table,  Fig.  51,  and  draw  along  as  before.  The  reading  of  the 


FIG.  51 

balance  will  be  the  same  as  in  the  first  case,  thus  showing  that 
the  friction  is  independent  of  the  area  of  the  surfaces  in  con- 
tact, (b)  Friction  is  independent  of  the  speed  with  which  one 
body  moves  over  another,  unless  the  motion  be  very  small, 
(c)  Friction  is  proportional  to  the  force  with  which  the  surfaces 
are  pressed  together.  Thus  if  one  brick  drawn  over  the  table 
offers  a  given  resistance,  two  bricks,  one  placed  upon  the  other, 
will  offer  twice  as  much  resistance  (friction). 

Friction  may  be  reduced  by  the  use  of  lubricating  oils,  or  in 
the  case  of  rolling  friction  by  the  use  of  "ball  bearings/'  Fig. 
52,  as  now  universally  employed  in  the  bicycle. 

97.  Efficiency  of  Machines.  The  efficiency  of  a  machine  is 
the  ratio  of  the  work  put  into  it  to  the  useful  work  gotten  out  of 
it.  This  is  expressed  as  follows: 


MECHANICS  OF   SOLIDS  59 

work  out 


Efficiency  = 


work  in 


If  a  machine  deliver  60  foot  pounds  of  useful  work  for  every 
100  foot  pounds  put  into  it,  its  efficiency  is  -f^  =  60  per  cent. 
This  means  that  40  per  cent  of  the  energy  was  lost  through 
friction  or  other  sources.  A  perfect  machine,  that  is,  one  oper- 
ating without  friction,  would  have  an  efficiency  of  100  per 
cent.  Since  it  is  impossible  to  make  such  a  machine,  the  work 
done  by  a  machine  is  always  less  than  the  work  put  into  it. 

98.  Law  of  Machines.  In  accordance  with  the  law  of  the 
conservation  of  energy,  the  work  done  by  a  force  acting  on  a 
machine  must  equal  the  work  done  by  the  machine.  This 


FIG.  52  FIG.  53 

principle,  as  applied  in  mechanics,  is  expressed  by  the  general 
law  of  machines:  The  force,  multiplied  by  the  distance  through 
which  it  acts,  is  equal  to  the  resistance  overcome,  multiplied 
by  the  distance  through  which  it  acts.  This  statement  of  the 
law,  of  course,  takes  no  account  of  friction. 

Experiment.  The  general  law  of  machines  may  be  demon- 
strated as  follows:  Weight  the  end  of  a  rod  so  that  it  will  bal- 
ance about  some  point,  for  example  one-third  of  the  distance 
from  one  end,  Fig.  53.  'This  constitutes  a  simple  machine.  To 
one  end  of  the  lever  thus  formed  suspend  a  mass  of  1  unit  F, 
and  to  the  other  end  2  units  R.  The  system  is  in  equilibrium. 
Now  if  F  be  moved  through  a  distance  s,  R  will  move  through 
a  distance  s'.  Now,  from  the  law  of  machines,  we  may  write 

Fs  =  Rs',  and  also, 
Fd  =  Rdf 


60 


HIGH   SCHOOL  PHYSICS 


FIG.  54 


in  which  F  is  the  force  and  d  the  force  arm;  R  the  resistance 
overcome  and  d'  the  resistance  arm. 

99.  Mechanical  Advantage.     Three  advantages  may  be  de- 
rived from  a  machine,     (a)  We  may  apply  a  force  in  the  most 

advantageous  direction,  as  in 
the  lifting  of  a  weight,  Fig. 
54.  (b)  We  may  gain  in 
speed  at  the  expense  of 
force,  as  in  the  gearing  of 
a  bicycle,  (c)  We  may  use 
a  small  force  to  overcome  a 
large  resistance,  as  in  the 
case  of  lifting  a  heavy  weight 
by  means  of  a  lever. 

When  we  speak  of  mechan- 
ical advantage  we  usually 
refer  to  the  third  advantage 
mentioned  above.  Mechani- 
cal advantage  is  the  ratio  of  the  resistance  overcome  to  the  force 
applied;  that  is, 

mechanical  advantage  =  -~  =  -j-, 

100.  Simple  Machines.     There  are  six  so-called  mechanical 
powers  or  simple  machines,  as  follows:   The  lever,  wheel  and 
axle,  inclined  plane,  pulley,  wedge,  and  screw.     All  forms  of 
mechanical  machines  (Supplement,  548),  however  complex,  may 
be  reduced  in  principle  to  one  or  more  of  these  simple  types. 

In  elementary  physics  it  is  customary,  in  solving  problems 
relating  to  simple  machines,  to  consider  the  friction  factor  as 
negligible  and  to  assume,  usually,  that  the  parts  of  a  machine 
are  rigid  and  without  weight.  When  these  factors  are  taken 
into  account,  problems  relating  to  machines  are  sometimes  very 
complicated  and  require  for  solution  the  principles  of  advanced 
mechanics. 


MECHANICS  OF   SOLIDS  61 

101.  The  Lever.  A  lever  is  a  rigid  bar  capable  of  moving 
about  a  fixed  point  called  a  fulcrum.  There  are  three  classes 
of  levers,  as  shown  in  Fig.  55,  in  which  F  is  the  force  applied 


t      t 

1          1 


R  F 

t     v 


FIG.  55 

to  one  end,  R  the  resistance  overcome,  0  the  fulcrum,  d  the 
force  arm,  and  d'  the  resistance  arm. 

Notes  on  the  lever.     The  following  points  should  be  noted 
with  respect  to  the  lever: 

1.  The  force  arm  d  is  measured  from  the  point  of  application 
of  the  force  F  to  the  fulcrum  0;  the  resistance  arm  d'  from  the 
resistance  R  to  the  fulcrum. 

2.  In  the  case  of  a  bent  lever  the  arms  d  and  d'  are  meas- 
ured from  the  fulcrum  to  the  lines  of  direc- 

tion F  and  R,  and  at  right  angles  to  the 
same,  Fig.  56. 

3.  Since  for  levers  of  the  same  length  the  pIG 
force  arm  d  is  the  greatest  for  the  second 

class,  it  follows  that  for  a  given  length,  a  lever  of  the  second 
class  offers  the  greatest  mechanical  advantage,  as  may  be  seen 
in  Fig.  55. 

4.  A  lever  of  the  third  class  gives  an  advantage  in  speed  at 
the  expense  of  the  force  applied. 

5.  The  product  of  the  force  into  its  lever  arm  is  called  the 
moment  of  the  force.     Moment  of  a  force  =  Fd.     In  the  study 
of  advanced  mechanics  the  moment  of  a  force  is  a  factor  of 
great  importance. 

6.  The  law  of  the  lever  is  that  of  the  general  law  of  machines; 
namely, 

Fd  =  Rd' 

EXERCISES.    28.    Classify  the  levers  of  Figs.  57,  58,  59  with  respect  to 
class. 


62 


HIGH   SCHOOL  PHYSICS 


29.  If  the  man  of  Fig.  60  exert  a  force  of  100  Ibs.  on  the  lever,  5  ft.  from 
the  fulcrum  F,  what  weight  can  be  lifted,  provided  the  weight  arm  R  is 
18  in.  in  length? 


FIG.  58 


FIG.  59 


FIG.  60 


FIG.  61 


30.  If  a  weight  of  300  Ibs.  act  downward  at  the  point  M,  Fig.  61,  1  ft. 
from  the  axis  of  the  wheel  (fulcrum),  what  upward  force  must  the  man 
exert,  providing  the  distance  from  M  to  his  hands  is  2  ft.? 


FIG.  62 


FIG.  63 


MECHANICS   OF   SOLIDS 


63 


FIG.  64 


102.  The  Wheel  and  Axle.  The  wheel  and  axle  is  an  appli- 
cation of  the  principle  of  the  lever.  The  large  disc,  Fig.  62,  is 
the  wheel;  the  small  shaded  disc  is 
the  axle.  The  force  F  is  applied  to 
a  rope  passing  over  the  wheel;  the 
resistance  or  weight  R  is  lifted  by 
means  of  a  rope  wound  around  the 
axle.  The  center  of  the  system  0  is 
the  fulcrum,  d  the  force  arm,  and  d' 
the  resistance  arm.  The  law,  as  in 
the  case  of  the  lever,  is  Fd  =  Rdf. 
Since  the  radii  of  the  two  wheels  are 
proportional  to  their  diameters,  and 
also  to  their  circumferences,  we  may 
write  r  :  r'  =  d  :  d'  =  c:  cf.  These  values,  therefore,  may  be 
substituted  for  d  and  d'  in  the  equation  Fd  =  Rdf . 

Other  forms  of  the  wheel  and  axle  are  seen  in  the  train  of 

cogwheels,  Fig.  63,  and  in  the  windlass,  Fig.  64. 
EXERCISES.    31.   What  force  applied  at  F,  Fig.  62, 

will  support  a  weight  of  100  Ibs.,  if  the  radius  of  the 

large  wheel  be  2  ft.  and  that  of  the  small  wheel  (axle) 

6  in.? 

32.  Suppose  that  for  a  given  wheel  and  axle,  similar 
to  that  of  Fig.  62,  the  circumference  of  the  wheel  is 
5  ft.     Find  the  circumference  of  an  axle  such  that  a 
force  of  20  Ibs.  will  support  a  weight  of  100  Ibs. 

33.  If  the  length  of  the  lever  arm  A  of  the  windlass, 
Fig.  64,  is  1.5  ft.,  and  the  circumference  of  the  axle  is 
1.5  ft.,  what  weight  will  be  supported  by  a  force  of 
10   Ibs.?      When    the   handle    makes    one    revolution, 
through  what  distance  will  the  weight  attached  to  the 
rope  move? 

103.   The  Pulley.     A  pulley  is  a  wheel  turn- 
ing about  an  axis  in  a  frame  or  block.     A  set 
of  blocks  containing  one  or  more  pulleys  each, 
together  with  the  attached  rope,  is  called  a 
FIG.  65  block  and  tackle,  Fig.  65. 


64 


HIGH   SCHOOL  PHYSICS 


With  respect  to  the  point  of  support,  pulleys  are  of  two  kinds, 
fixed  and  movable.  A  fixed  pulley  is  one  that  is  fixed  or 
fastened  to  a  stationary  support,  as  a  beam  or  wall.  A  mov- 
able pulley  is  one  that  is  attached  to  the  weight  or  object  to 
be  moved.  Fig.  66  illustrates  a  system  of  one  fixed  and  one 
movable  pulley. 

When  F  moves  through  a  distance  d,  R  moves  through  d'\ 
hence  the  law  of  the  pulley  is 

Fd  =  Rd' 

104.  Mechanical  Advantage  of  the  Pulley.  Experiment. 
The  law  of  machines,  Fd  =  Rd',  may  be  experimentally 
verified  for  a  number  of  typical  cases  by  means  of  two  or 
three  pulleys  and  a  spring  balance,  arranged  as  in  the  follow- 
ing figures: 


FIG.  66 


FIG.  67 


FIG.  68 


FIG.  69 


1.  Fig.  67.    In  this  case  when  F  moves  down  one  unit  of 
distance,  R  moves  up  one  unit,  that  is  d  =  d' ',  and  hence  F  = 
R.     A  force  of  10  pounds,  for  example,  at  F  will  overcome  a 
resistance  at  R  of  10  pounds.     The  only .  advantage  gained 
by  the  use  of  the  fixed  pulley  is  in  the  change  of  direction  of 
the  force.     A  fixed  pulley  gives  no  mechanical  advantage. 

2.  Figs.  68,  69.     Since  we  have  here  two  ropes  attached  to 
the  movable  pulley  in  each  case,  F  will  move  2  units  of  space 


MECHANICS    OF    SOLIDS 


65 


for  R  1  unit;  hence  1  unit  of  force  at  F  will  support  2  units  of 
resistance  at  R.  A  force  of  10  pounds  at  F  will  exert  10  pounds 
at  F',  hence  20  pounds  at  R.  In  Fig.  69  the  fixed  pulley  P 
gives  no  mechanical  advantage;  it  serves  merely  to  change 
the  direction  of  F. 

3.  Fig.  70.  Here  three  ropes  are  attached  to  the  movable 
pulley.  When  F  moves  3  units  of  distance,  R  will  move  1  unit; 
therefore  10  pounds  of  force  at  F  will  exert  30  pounds  at  R. 

F 


FIG.  70 


FIG.  71 


FIG.  72 


EXERCISES.    34.   A  force  of  10  units  at  F,  Fig.  71,  will  balance  how 
many  units  of  resistance  at  R! 

35.   A  force  of  10  Ibs.  at  F,  Fig.  72,  will  support  what  weight  at  R  ? 

105.  The  Inclined  Plane.  The  inclined  plane  is  a  common 
device  for  lifting  heavy  bodies  through 
a  vertical  height  by  sliding  or  rolling 
them  along  an  incline,  Fig.  73.  There 
are  three  important  cases  relating  to 
problems  of  the  inclined  plane. 

1 .  The  force  applied  parallel  to  the 
incline,  Fig.  74.  The  equation  Fd  = 
Ed'  applies  here,  where  d  =  AC,  the 
length  of  the  incline,  and  d'  =  BC, 
the  vertical  height  through  which  the  weight  is  lifted. 


FIG.  73 


66 


HIGH   SCHOOL  PHYSICS 


2.  The  force  applied  parallel  to  the  base,  Fig.  75.  In  this 
case  the  force  distance  d  is  equal  to  the  length  of  the  base  AB 
and  d'  =  BC  as  before. 


B    A 


B    A 


FIG.  74 


FIG.  75 


FIG.  76 


3.  The  force  applied  at  an  angle,  Fig.  76.  The  solution  of 
problems  of  this  class  requires  that  the  force  be  resolved  into  a 
component  along  the  incline  or  base  and  solved  as  above. 

Since  the  force  distance  d  is  greatest  in  case  1,  it  follows  that 
the  greatest  mechanical  advantage  is  obtained  in  the  case  of  an 
inclined  plane  when  the  force  is  applied  parallel  to  the  incline. 

EXERCISES.  36.  What  force  applied  parallel  to  the  incline  will  be 
required  to  support  a  200  Ib.  weight  on  a  smooth  plane,  the  incline  of  which 
is  16  ft.,  and  the  vertical  height  4  ft.? 

37.  What  force  applied  parallel  to  the  base  of  the  plane  of  exercise  36 
will  be  required  to  support  the  weight? 

106.  The  Wedge.     A  wedge  is  a  modified  form  of  an  inclined 
plane.     It  may  be  considered  as  being  made  up  of  two  planes 
placed  base  to  base.     The  blade  of  a  pocket  knife,  the  end  of 
a  nail,  the  point  of  a  needle  are  all  wedge-shaped  instruments. 
The  wedge  is  usually  used  to  overcome  great  resistance  through 
small  spaces,  as  in  the  splitting  of  logs,  the  lifting  of  heavy 
weights  through  very  small  distances,  etc.     Since  the  force  is 
usually  applied  to  the  wedge  by  means  of  a  blow  from  a  hammer 
or  sledge,  and  the  friction  factor  is  very  large  and  cannot  be 
neglected,   it   is   not   possible   to  express  a   definite  relation 
between  the  force  and  the  resistance,  as  stated  in  the  general 
law  of  machines. 

107.  The   Screw.     A  screw   is  a  cylinder  having  a  spiral 
groove  cut  around  its  circumference,  Fig.  77.     The  spiral  ridge 
is  called  the  thread  and  the  distance  between  two  consecutive 


MECHANICS   OF    SOLIDS  67 

threads  the  pitch.  The  mechanical  advantage  of  the  screw  is 
derived  from  a  combination  of  the  principles  of  the  lever  and 
the  inclined  plane.  Fig.  78  shows  one  form  of  the  screw. 
The  force  is  applied  at  the  point  F  on  the  circumference,  and 
the  resistance  to  be  overcome  by  the  downward  thrust  is  at  R. 
The  force  distance  d  is  the  circumference  of  the  circle  swept 
out  by  the  force  F  in  making  one  complete  revolution;  the 
resistance  distance  d'  is  the  distance  between  two  consecutive 
threads,  that  is,  the  pitch.  For  one  complete  revolution  of 
F,  R  moves  downward  one  thread  unit. 


FIG.  77  FIG.  78  FIG.  79 

EXERCISES.  38.  If  a  force  of  20  Ibs.  applied  to  the  circumference  of 
the  wheel,  Fig.  78,  act  through  a  distance  of  3  ft.  in  making  one  complete 
revolution,  and  thus  cause  the  screw  to  move  downward  J  in.,  what  will 
be  the  resistance  overcome  at  Rt 

39.  The  lever  W F  of  the  jack  screw,  Fig.  79,  is  1  meter  in  length.  If 
one  revolution  of  the  force  cause  the  screw  to  move  upward  1  cm.,  what 
resistance  will  be  overcome  by  a  force  of  10  kg.? 

EXERCISES  AND  PROBLEMS  FOR  REVIEW 

1.  Define  and  illustrate  centripetal  force;    centrifugal  force. 

2.  Explain  the  use  of  the  following  equation  and  state  the  meaning 

of  each  term  contained  therein:    F  = Does  this  equation  give 

results  in  absolute  or  gravitational  units? 

3.  A  mass  of  2  Ibs.  is  attached  to  a  string  2  ft.  in  length  and  is  rotated 
with  a  linear  velocity  of  5  ft.  per  second.     Find  the  centrifugal  force  which 
it  exerts  in  pounds. 

4.  Distinguish   between    gravitation    and    gravity.     Explain   why   a 
body  weighs  less  at  the  equator  than  at  the  poles. 


68  HIGH   SCHOOL   PHYSICS 

6.  Define  center  of  gravity.  Locate  the  center  of  gravity  (a)  in  a 
homogeneous  rectangular  block;  (b)  circular  disc;  (c)  triangular  piece  of 
board. 

6.  Explain  how  to  find  the  center  of  gravity  of  an  unsymmetrical 
body,  such  as  a  piece  of  board  of  irregular  shape. 

7.  Define  stable,  unstable,  and  neutral  equilibrium,  and  give  illus- 
trations of  each. 

8.  In  how  many  ways  may  the  stability  of  a  body  be  increased? 
Make  drawing  to  illustrate  and  explain  why  a  rectangular  body  lying  on 
its  side  is  more  stable  than  when  standing  on  end. 

9.  Define  line  of  direction,  and  explain  the  relation  of  this  line  to  the 
base  of  a  body  with  reference  to  its  stability. 

10.  Define:   Simple  pendulum,  compound  pendulum,  simple  vibration, 
complete  vibration,  period,  amplitude. 

11.  Explain  how  to  find  by  experiment  the  center  of  oscillation  of  a 
compound  pendulum;    the  center  of  percussion. 

12.  How  is  the  period  of  the  pendulum  affected  (a)  when  its  length  is 
increased?     (b)  When  the  force  acting  upon  it  is  increased? 

13.  Consider  a  pendulum  consisting  of  a  spherical  metal  bob  attached 
to  a  string.   What  is  the  relation  of  its  period  to  (a)  its  amplitude?    (b)  the 
mass  of  the  bob? 

14.  A  given  pendulum  makes  240  vibrations  in  2  minutes.     What  is 
its  frequency  (number  of  vibrations  per  second)?     (b)  What  is  its  period 
(time  of  one  vibration)? 

15.  Explain  the  use  of   the   following  equation  and  the  meaning  of 

each  term:  T  = 

16.  Find  the  period  of  a  simple  pendulum  (a)  4  meters  in  length; 
(b)  4  ft.  in  length. 

17.  Define:    Work,  power,  energy,  potential  energy,  kinetic  energy. 

18.  Explain  the  following  equations,  giving  the  meaning  of  each  term: 

W  =  Fs;  P  =  j;  P.E.  =  Fs;  K.E.  =  f  mv*. 

19.  Two  men,  A  and  B,  are  at  work  carrying  coal  into  a  cellar.     A 
carries  1  ton  into  the  cellar  in  1  hour;    B  carries  1  ton  in  an  hour  and  a 
quarter,     (a)  Which  man  does  the  greater  amount  of  work?     (b)  Which 
works  at  the  greater  rate? 

20.  Define:  Foot  pound,  gram  centimeter,  kilogram  meter,  foot  poundal, 
erg,  horse  power,  watt,  kilowatt. 

21.  A  weight  of  1  ton  is  lifted  to  a  height  of  55  ft.  in  10  minutes,     (a) 
Find  the  work  done  in  foot  pounds,     (b)  At  what  rate  is  the  work  done  in 
horse  power? 


MECHANICS    OF    SOLIDS  69 

22.  A  weight  of   179,040  kilograms  is  lifted  to  a  height  of   10  meters 
in  2  minutes.     Find  the  rate  at  which  the  work  is  done  in  (a)  watts; 
(b)  kilowatts;    (c)  H.P. 

23.  A  stone  weighing  2  Ibs.  is  thrown  upward  to  a  height  of  20  ft.     At 
what  point  does  it  have  (a)  its  greatest  kinetic  energy?    (b)  its  greatest 
potential  energy?     Explain  the  relation  between  the  potential  and  the 
kinetic  energy  which  the  stone  possesses  at  any  instant  during  its  upward 
or  downward  motion. 

24.  What  work,  in  foot  pounds,  was  done  on  the  stone  (problem  23)  in 
order  to  elevate  it  to  a  height  of  20  ft.?     What  is  its  potential  energy  when 
at  the  highest  point?     How  does  the  P.E.  which  it  possesses  at  its  highest 
point  compare  with  the  K.E.  it  will  have  when  it  strikes  the  ground? 

25.  A  body  having  a  mass  of  10  grams  has  a  velocity  of  5  meters  per 
second.     Find  its  kinetic  energy  in  (a)  ergs;    (b)  gram  centimeters. 

26.  A  mass  of    10  Ibs.  has  a  velocity  of  5  ft.  per  second.     Find  its 
kinetic  energy  in  (a)  absolute  units;    (b)  gravitational  units. 

27.  A  bullet  having  a  mass  of  1  oz.  strikes  a  target  with  a  velocity  of 
500  ft.  per  second.     What  is  the  K.E.  of  the  bullet  in  foot  pounds? 

28.  State  the  law  of  machines,  and  explain  each  term  in  the  equation 
Fd  =  Rdf. 

29.  Make  drawings  to  illustrate  the  three  classes  of  levers,  and  write 
a  problem  applicable  to  each. 

30.  Draw  three  pulleys  as  shown  in  Fig.  70,  and  find  what  force  will 
be  required  to  support  a  weight  of  600  Ibs. 

31.  Draw  four  pulleys  as  shown  in  Fig.  71,  and  find  what  force  will  be 
required  to  support  a  weight  of  600  Ibs. 

32.  A  man  desiring  to  place  a  barrel  upon  a  platform  4  ft.  high  uses 
as  an  incline  a  plank  12  ft.  in  length.     He  rolls  the  barrel  up  the  plank. 
What  force  applied  parallel  to  the  incline  will  be  required  to  support  the 
barrel  upon  the  plank? 

33.  A  man  lifts  a  weight  by  means  of  a  jack  screw,  the  distance  between 
the  threads  of  which  is  £  in.     That  is,  for  every  turn  of  the  screw  the 
weight  is  lifted  |  of  an  inch.     The  lever  arm  of  the  screw  (see  Fig.  79)  is 
3  ft.  in  length.     What  weight  is  the  man  capable  of  lifting  if  he  exerts  a 
force  of  100  Ibs.? 

For  additional  Exercises  and  Problems,  see  Supplement. 


CHAPTER  IV 
MECHANICS    OF   FLUIDS 

PROPERTIES  OF  FLUIDS 

108.  Definitions.     A  fluid  is  a  substance  which  will  flow. 
Fluids  are  divided  into  liquids  and  gases.     A  liquid  is  a  fluid 
which  conforms  to  the  shape  of  the  vessel  containing  it  and 
which  has  a  definite  surface.     A  gas  is  a  fluid  which  tends  to 
fill  the  containing  vessel  and  which  has  no  definite  surface. 
Mists,  fogs,  and  clouds  are  fluids  which  consist  of  finely  divided 
particles  of  liquid.     The  term  vapor  is  used  by  different  writers 
in  different  senses.     It  is  ordinarily  employed  to  designate  a 
gas  which  has  been  formed  from  a  liquid  or  solid;    thus  we 
speak  of  water  vapor  in  the  air,  meaning  thereby  water  in  a 
gaseous  form. 

Hydrostatics  treats  of  the  pressure  of  liquids  at  rest.  Hy- 
draulics treats  of  liquids  in  motion.  Pneumatics  treats  of  the 
pressure  and  motion  of  gases.  Pressure  is  force  per  unit  area. 
(Supplement,  549.) 

109.  Properties   of  Fluids.     1.   Fluids  are  perfectly  elastic. 
If  a  fluid  such  as  air  or  water  in  a  containing  vessel  be  subjected 
to  a  compressing  force,  its  volume  will  diminish;   if  the  com- 
pressing force  be  removed  the  fluid  will  exactly  regain  its  origi- 
nal shape  and  volume;  hence  we  say  that  fluids  are  perfectly 
elastic. 

2.  Fluids  transmit  pressure  equally  in  all  directions.  If  a 
force  be  applied  to  a  solid,  the  body  tends  to  move  in  the  direc- 
tion of  the  force.  If  a  force  be  applied  to  a  fluid,  the  force  is 
transmitted,  not  in  one  direction  as  in  the  case  of  the  solid,  but 


MECHANICS  OF   FLUIDS 


71 


FIG.  80 


in  all  directions.     Consider  a  vessel  to  be  filled  with  highly  elas- 
tic circular  hoops,  as  shown  in  Fig.  80.     These  hoops  may  be 
assumed    to    have    the    properties   of  a 
fluid.     A  force  applied  at  F  is  transmit- 
ted equally  in  all  directions. 

3.  Fluids  are  compressible.  Gases  are 
highly  compressible,  differing  in  this  re- 
spect in  a  very  marked  degree  from  liq- 
uids, which  are  only  slightly  compressible. 
For  a  pressure  of  1  atmosphere  water  is 
reduced  only  by  TO  iou  °f  its  volume,  while 
air  is  reduced  by  ?  for  the  same  pressure. 

In  all  ordinary  problems,  liquids  are  considered  as  being  prac- 
tically incompressible. 

110.  Pascal's  Law.  The  law  relating  to  the  transmission  of 
pressure  by  fluids  was  first  definitely  stated 
by  Pascal,  a  French  scientist.  Pascal's  law 
may  be  stated  as  follows:  Pressure  applied 
to  a  given  area  of  a  fluid  enclosed  in  a  vessel 
is  transmitted  undiminished  to  every  equal 
area  of  the  vessel.  Pascal  performed  a  strik- 
ing experiment  to  demonstrate  the  appli- 
cation of  this  law.  A  long  tube  was  firmly 
fixed  into  the  head  of  a  stout  cask,  Fig.  81. 
Both  cask  and  tube  were  then  filled  with 
water.  The  weight  of  the  water  in  the 
tube  exerted  a  force  on  the  cask  as  many 
times  greater  than  itself  as  the  inner  area 
of  the  cask  was  greater  than  the  cross  sec- 
tional area  of  the  tube.  The  force  exerted 
by  the  water  in  the  tube  was  sufficient  to 
burst  the  vessel. 


FIG.  81 


EXERCISES.  1.  A  jug,  Fig.  82,  is  filled  with  water. 
If,  by  means  of  a  lever,  a  force  of  10  Ibs.  be  exerted 
on  the  cork,  cross  sectional  area  1  sq.  in.,  what  will 


72 


HIGH   SCHOOL   PHYSICS 


be  the  total  force  transmitted  to  the  vessel  if  its  interior   surface  be 
100  sq.  in.? 

2.    If  the  cross  sectional  area  of  the  cork  of  exercise  1  were  j  sq.  in., 
-m  what  would  be  the  total  force  exerted  on  the 

sides  of  the  jug? 

111.  Hydraulic  Press.  An  impor- 
tant application  of  the  principle  stated 
by  Pascal's  law  is  found  in  the  opera- 
tion of  the  hydraulic,  or  hydrostatic 
press.  This  machine  is  used  where  it 
is  desirable  to  exert  enormous  force,  such  as  in  the  compres- 
sion of  material  into  very  small  space  for  economy  in  shipment, 
for  the  lifting  of  heavy  locomotives  that  have  jumped  the 
track,  etc. 


tf                               n 

A 

k    } 

U 

i                   i 

FIG.  82 

F 


FIG.  83 


FIG.  84 


A  sectional  outline  of  a  hydraulic  press  is  shown  in  Fig.  83. 
The  tank  A  contains  a  liquid  which  is  driven  by  the  force  pump 
P  into  the  cylinder  C,  thus  acting  on  the  piston  P',  driving  it 
upward.  The  force  exerted  upon  the  large  piston  P'  is  as  many 


MECHANICS  OF  FLUIDS  73 

times  greater  than  that  exerted  on  the  liquid  in  the  force  pump 
P  as  the  cross  sectional  area  of  P'  is  greater  than  P. 

EXERCISES.  3.  Suppose  that  the  cross  sectional  area  of  P  is  2  sq.  in. 
and  that  of  P'  is  200  sq.  in.  A  force  of  10  Ibs.  applied  to  the  small  piston 
P  will  exert  what  upward  force  on  P'  ? 

4.  A  force  of  500  Ibs.  is  exerted  downward  upon  the  small  piston  of  a 
hydrostatic  press,  the  cross  sectional  area  of  the  piston  being  2  sq.  in. 
This  force  is  transmitted  through  the  liquid  to  the  large  piston,  the  cross 
sectional  area  of  which  is  200  sq.  in.  What  upward  force  is  exerted  upon 
the  large  piston? 

PRESSURE  DUE  TO  LIQUIDS 

112.  Pressure  in  a  Liquid.  The  facts  relating  to  the  pres- 
sure exerted  at  any  point  in  a  liquid  may  be  stated  as  follows: 

1.  Pressure  in  a  liquid  is  proportional  to  the  depth.     Experi- 
ment.    This  can  be  shown  by  thrusting  a  bent  glass  tube  con- 
taining mercury  down  into  the  water  enclosed  in  a  tall  glass 
jar,  Fig.  84.     As  the  curved  portion  of  the  tube  moves  down- 
ward from  a  to  b}  the  mercury  is  depressed  in  the  arm  c,  due 
to  the  increased  pressure  upon  it.     If  the  pressure  at  a  given 
depth  be  10  pounds  per  square  inch,  then  at  twice  the  depth 
it  will  be  20  pounds  per  square  inch,  and  so  on. 

2.  Pressure  is  proportional  to  the  density  of  the  liquid.      Mer- 
cury is  13.6  times  as  heavy  as  water;  therefore,  for  a  given  depth, 
mercury  will  exert  13.6  times  as  great  a 

pressure  as  water. 

3.  Pressure    at  a  point  is  equal   in  all 
directions.     This    fact  may   be   shown  by 
thrusting  three  bent  tubes  containing  mer- 
cury into  a  vessel  of  water,  Fig.  85.     The 
lower  openings  of  the  tubes  are  all  in  the 

same   plane,   but    communicate  with    the  pIG  85 

water  in  different  directions.     The  depres- 
sion of  the  mercury  in  each  tube  is  the  same,  showing  that 
the  pressure  in  all  three  directions  in  the  plane  ab  is  the  same. 


74  HIGH   SCHOOL  PHYSICS 

113.  Force  Exerted  by  a  Liquid  upon  the  Surface.  The 
total  force  exerted  by  a  liquid  upon  a  submerged  surface  de- 
pends upon  (a)  the  area  of  the  surface,  (b)  the  depth  of  the  liquid 
pressing  upon  the  surface,  and  (c)  the  density  of  the  liquid. 
The  total  force  exerted  by  a  liquid  upon  an  immersed  surface 
is  written, 

F  =  AHD 

in  which  F  is  the  force  in  gravitational  units,  A  the  area  of  the 
surface  pressed  upon,  H  the  height  of  the  surface  of  the  liquid 
above  the  center  of  figure  (Supplement,  550),  and  D  the  den- 
sity of  the  liquid.  The  above  equation  applies  to  all  submerged 
surfaces  whether  vertical,  horizontal,  or  inclined;  plane  or 
curved.  In  elementary  physics  two  cases  are,  in  general, 
considered. 

1.  Force  on  the  bottom  of  a  vessel.  The  force  exerted  by  a 
liquid  upon  the  bottom  of  a  vessel  having  a  horizontal  base  is 

force  =  area  of  base  X  height  of  vessel  X  density  of  liquid, 
F  =  AHD 

1  2.  Force  on  the  side  of  a  vessel.  The  force  exerted  by  a 
liquid  upon  a  vessel  having  vertical  sides  varies  directly  with 
the  depth  of  the  liquid.  At  the  surface  the  force  is  zero;  at 
the  bottom  it  is  a  maximum.  The  force  has  an  average  value 
at  one-half  the  depth;  hence  we  may  write, 

force  =  area  of  the  side  X  one-half  the  height  X  density, 


The  density  of  distilled  water  at  4°  C.  is  1  gram  per  cubic 
centimeter;  this  is  equivalent  to  about  62.5  pounds  per  cubic 
foot.  In  solving  problems  relating  to  water  pressure  it  is 
generally  assumed,  however,  unless  stated  specifically  to  the 
contrary,  that  the  density  of  water  =  1  gram  per  cubic 
centimeter  =  62.5  pounds  per  cubic  foot. 


MECHANICS   OF   FLUIDS 


75 


EXERCISES.    5.   Find  the  force  in  grams  exerted  on  the  bottom  of  a 
vessel  10  cm.  on  each  edge,  when  filled  with  water. 

6.  Find  the  force  exerted  on  the  bottom  of  a  vessel  10  ft.  on  each  edge, 
when  filled  with  water. 

7.  Find  the  force  exerted  on  the  bottom  of  a  vessel  10  ft.  on  each  edge, 
when  filled  with  brine,  density  1.2  times  that  of  water. 

8.  Find  the  force  exerted  on  the  bottom  of  the  vessel  mentioned  in 
exercise  5,  when  filled  with  mercury,  density  13.6. 

9.  Find  the  force  exerted  on  one  side  of  the  vessel  mentioned  in  (a) 
exercise  5;    (b)  exercise  6. 

114.   The  Hydrostatic  Paradox.     We  have  just  learned  from 
the  preceding  topic  that  the  force  exerted  by  a  liquid  on  the 


FIG.  86 

bottom  of  a  vessel  depends  only  on  the  area  of  the  bottom, 
the  depth  of  the  liquid,  and  its  density.  That  is,  the  pres- 
sure is  independent  of  the  shape  of  the 
vessel.  This  is  called  the  hydrostatic 
paradox.  If  three  vessels,  A,  B,  C,  Fig. 
86,  having  bottoms  of  the  same  area,  are 
filled  to  the  same  depth  with  a  given 
liquid,  the  downward  force  exerted  on  e 
the  bottom  of  each  vessel  will  be  the 
same.  In  A  the  force  on  the  bottom  is 
equal  to  the  weight  of  the  liquid;  in  B 
the  force  is  less  than  the  weight  of  the 
liquid;  in-  C  the  force  is  greater  than  the  weight  of  the 
liquid.  This  can  be  demonstrated  by  means  of  three  vessels, 
as  shown  in  Fig.  87.  The  bottoms  of  the  vessels  have  equal 
areas.  The  tube  T  contains  mercury,  which  stands  at  the 


FIG.  87 


76 


HIGH  SCHOOL  PHYSICS 


level  cd.  When  vessel  A  is  screwed  upon  the  standard  at  d 
and  is  filled  with  water,  the  mercury  falls  in  one  arm  and  rises 
in  the  other  from  c  to  e,  the  height  ce  measuring  the  down- 
ward force  at  d.  If  now  the  vessels  'B  and  C  be  placed  suc- 
cessively upon  the  standard  d  and  filled  with  water  to  the  level 
ab,  the  mercury  in  each  case  will  rise  to  e,  thus  showing  that 
the  force  is  independent  of  the  shape  of  the  vessel. 

The  explanation  of  the  hydrostatic  paradox  lies  in  the  state- 
ment of  Pascal's  law;  namely,  that  the  pressure  on  a  given 
area  of  the  bottom,  due  to  the  weight  of  a  column  of  liquid,  is 
transmitted  undiminished  to  every  like  area.  For  example, 
force  exerted  by  the  column  beef  of  vessel  C,  Fig.  86,  is 
transmitted  to  the  areas  ab  and  cd.  That  is,  the  force  exerted 
on  the  bottom  of  the  vessel  C  is  the 
same  as  if  the  sides  were  vertical. 

115.  Communicating  Tubes.  If 
water  be  poured  into  a  vessel  having 
two  or  more  communicating  tubes,  Fig. 
88,  it  will  rise  to  the  same  level  in  each, 
no  matter  what  the  shape  of  the  vessel. 
We  say  that  "  water  seeks  its  level."  A 
good  illustration  of  this  principle  is  fur- 
nished by  the  water  in  a  tea  kettle  or 
tea  pot,  Fig.  89.  This  follows  because 
the  pressure  is  proportional  to  the  depth  and  is  independent 
of  the  shape  of  the  vessel.  The  principle  that  water  will  seek 
its  level  holds  only  for  liquids  at  rest.  When  water  is  flowing 


FIG.  88 


FIG.  89 


FIG.  90 


MECHANICS   OF   FLUIDS 


77 


from  an  opening,  the  pressure,  and  hence  the  level,  decreases 
as  the  opening  is  approached,  as  shown  in  Fig.  90.  In  case 
the  opening  at  c  be  closed,  the  water  in  all  the  tubes  will  rise 
to  a  common  level. 

116.    City   Water   Supply.     An   application  of  the  principle 
illustrated  by  liquids  in  communicating  tubes  is  sometimes 


FIG,  91 

found  in  the  method  of  supplying  towns  and  cities  with  water. 
Fig.  91  illustrates  such  a  system,  in  which  water  is  conducted, 
by  means  of  pipes  or  "mains,"  from  the 
source  of  supply  through  an  aqueduct  and 
thence  underground  to  the  gardens  and 
houses  beyond.  The  water  in  the  foun- 
tain rises  theoretically  to  the  level  of  the 
source,*  but  practically  not  so  high  on  ac- 
count of  the  friction  due  to  the  air  and 
the  pipes.  Where  there  is  no  natural  ele- 
vated source  of  supply,  it  is  necessary  to 
pump  the  water  from  wells  into  reservoirs 
or  standpipes,  Fig.  92,  situated  usually 
upon  high  ground,  from  which  it  is  dis- 
tributed to  the  consumers.  In  some  cities 
no  reservoirs  are  used,  the  pumping  engine 
being  so  adjusted  as  to  supply  the  water 
at  the  required  pressure. 

117:   Artesian  Wells.     The  tendency  of 
water   to    seek   its    level   is  further  illus- 


FIG.  92 

Standpipe,  Lancas- 
ter, Pa. 


trated  by  flowing,  or  artesian  wells.     Fig.  93  shows  the  condi- 


78 


HIGH   SCHOOL   PHYSICS 


tions  necessary  for  such  a  well.  The  first  stratum  is  of  loose 
soil;  b  is  an  impervious  layer  of  clay  or  rock;  c,  a  stratum  of 
gravel;  and  below  this  again  is  another  impervious  layer,  d. 
Water  flowing  from  a  height  is  confined  between  the  two  imper- 
vious strata  b  and  d  and  is  under  pressure.  When  this  vein  of 

B 

A 


FIG.  93.  —  Artesian  Wells 

water  is  tapped,  an  artesian  well  results.  An  artesian  well  is 
usually,  but  not  necessarily,  a  flowing  well;  both  A  and  B 
are  artesian  wells.  The  name  " artesian"  comes  from  the 
province  of  Artois,  in  France,  where  the  operation  of  drilling 
for  flowing  wells  was  first  performed. 

Sometimes  these  flowing  wells  occur  in  comparatively  level 
regions.  In  such  cases  the  height  of  land  which  furnishes  the 
pressure  may  lie  off  at  a  distance  of  a  number  of  miles.* 

118.  Water  Wheels.  One  of  the  oldest  methods  of  obtain- 
ing power  from  water  was  by  means  of  the  water  wheel,  the 

old-fashioned  and  picturesque  type, 
of  which  is  familiar  to  everyone. 
Modern  water  wheels  are  of  two 
general  types,  the  water  motor  and 
the  turbine  wheel. 

The  water  motor  is  often  used  in 
cities  where  water  is  delivered  in 
pipes  under  high  pressure.  Fig.  94 
gives  a  sectional  view  of  a  water 

motor.  Water  issues  with  great  velocity  from  the  pipe, 
striking  against  the  blades  of  the  wheel.  The  rotating  system 


MECHANICS   OF   FLUIDS 


79 


is  enclosed  in  a  metal  case,  from  which  the  water  flows  into 
a  waste  pipe. 

In  the  case  of  the  turbine  wheel  (Supplement,  551),  the  water 
enters  the  sides  through  a  number  of  openings  in  the  wheel 
case,  striking  against  the  blades  in  a  manner  somewhat  similar 
to  that  of  the  water  motor. 

Hydraulic  Elevator,  Hydraulic  Ram,  see  Supplement,  552. 

BUOYANCY  OF  LIQUIDS 

119.  Archimedes'  Principle.  Experiment.  If  a  stone  or 
piece  of  metal  be  weighed  in  air,  by  means  of  a  spring  balance, 
Fig.  95,  and  then  weighed  in  water,  it  will  be 
found  that  the  body  loses  weight  in  the  liquid. 
It  is  buoyed  up  by  the  liquid  in  which  it  is  im- 
mersed. Archimedes  (287-212,  B.  c.),  a  Greek 
philosopher,  of  Syracuse,  Sicily,  was  the  first  to 
announce  the  principle  of  buoyancy,  which  has 
come  to  be  called  the  principle  of  Archimedes, 
and  which  may  be  stated  thus :  A  body  immersed 
in  a  fluid  is  buoyed  up  by  a  force  equal  to  the  weight 
of  the  fluid  displaced.  According  to  tradition,  the 
manner  in  which  the  principle  of  buoyancy  was 
discovered  was  somewhat  as  follows :  Hiero,  King 
of  Syracuse,  possessed  a  golden  crown  which  he 
suspected  had  'been  adulterated  with  a  base 
metal  by  his  goldsmith.  He  applied  to  Archimedes  to  detect 
the  fraud.  The  solution  of  the  problem  was  suggested  to  the 
philosopher  while  he  was  in  one  of  the  public  baths  of  his  native 
city.  He  observed  the  buoyant  effect  of  the  water  upon  his 
body,  and  conceived  that  the  buoyant  force  was  equal  to  the 
weight  of  the  water  displaced.  He  at  once  perceived  that  the 
purity  of  the  crown  could  be  determined  by  comparing  its  spe- 
cific gravity,  as  determined  by  the  principle  of  buoyancy,  with 
that  of  pure  gold.  Greatly  delighted  with  his  discovery,  Archi- 
medes is  said  to  have  exclaimed,  " Eureka!"  (I  have  found  it!) 


FIG.  95 


80 


HIGH   SCHOOL   PHYSICS 


120.  The  Principle  Explained.  An  explanation  of  Archi- 
medes' principle  of  buoyancy  may  be  given  by  means  of  Fig. 
96.  Let  abed  be  one  face  of  a  cubical  block  of  unit  thickness 
immersed  in  water;  the  downward  force  acting  upon  the  upper 
face  of  the  block  is  equal  to  the  area  cd  times  the  depth  cf; 
that  is,  the  downward  force  on  the  block  is  equal  to  the  weight 
of  the  column  of  liquid  dcfe.  The  upward  force  acting  upon 
the  lower  face  of  the  block,  due  to  the  liquid,  is  equal  to  the 
area  of  ab  times  the  depth  of  the  liquid  bf;  that  is,  the  block  is 
buoyed  up  by  the  weight  of  a  column  of  liquid  proportional  to 
abfe.  The  upward  force  is  therefore  greater  than  the  down- 
ward force,  and  the  difference  between  the  two,  abfe  —  dcfe,  is 


J 


FIG.  96 


FIG.  97 


FIG.  98 


equal  to  the  weight  of  a  column  of  liquid  abed;  hence  we  say  that 
the  block  is  buoyed  up  by  the  weight  of  the  water  which  it  dis- 
places. Whether  a  body  immersed  in  a  fluid  will  sink  or  float  de- 
pends upon  the  relation  between  its  own  weight  and  the  weight 
of  the  fluid  displaced.  If  the  body  be  heavier  than  the  fluid  dis- 
placed, it  will  sink;  if  lighter,  it  will  float.  If  it  weighs  just 
as  much  as  the  fluid  displaced,  it  will  tend  neither  to  sink  nor 
float,  but  will  remain  stationary  in  the  fluid  wherever  placed. 

121.  Illustrations  of  Archimedes'  Principle.  Archimedes' 
principle  applies  to  bodies  that  float  equally  well  as  to  bodies 
that  sink.  A  body  that  floats  displaces  its  own  weight;  a  body 
that  sinks  displaces  its  own  volume.  One  of  the  most  direct 
methods  of  determining  the  truth  of  these  statements  would 
be  to  use  some  such  simple  device  as  shown  in  Figs.  97  and  98. 


MECHANICS  OF  FLUIDS  81 

Consider  first  the  case  of  a  body  that  is  lighter  than  water, 
as  for  example  a  block  of  wood.  Weigh  the  block  in  air  and 
then  place  it  in  a  beaker  full  of  water,  Fig.  97.  The  floating 
body  displaces  a  certain  amount  of  water  which  will  flow  out 
into  the  smaller  vessel,  and  which  can  then  be  weighed.  It 
will  be  found  that  the  weight  of  the  water  displaced  is  just 
equal  to  the  weight  of  the  floating  body.  Again,  consider  the 
case  of  a  body  that  is  heavier  than  water.  Weigh  the  body 
as  before  in  air,  and  then  drop  it  into  the  beaker  full  of  water. 
It  will  be  found  that  the  weight  of  the  water  displaced  in  this 
case  is  less  than  the  weight  of  the  body,  but  that  the  volume  of 
the  water  displaced  is  equal  to  the  volume  of  the  body  that 
sinks.  In  both  cases,  that  is,  for  the  light  body  as  well  as  for  the 
heavy,  the  buoyancy  exerted  by  the  liquid  is  equal  to  the 
weight  of  the  liquid  displaced. 

EXERCISES.  10.  A  piece  of  metal  having  a  volume  of  10  cc.  and  a  mass 
of  100  grams  will  displace  (a)  what  volume  of  water?  (b)  how  many  grams 
of  water?  (c)  will  be  buoyed  up  by  what  force  in  water?  (d)  will  have 
what  weight  in  water? 

11.  Let  a  cubic  foot  of  lead  weighing  710  Ibs.  in  air  be  immersed  in 
water,     (a)  What  volume  of  water  will  it  displace?     (b)  What  weight  of 
water  will  it  displace?     (c)  What  buoyant  force  will  act  upon  it?     (d) 
What  will  be  its  weight  in  water? 

12.  A  cubic  foot  of  a  given  substance  weighing  60  Ibs.  is  thrown  into 
water,     (a)  Will  it  sink  or  float?     (b)  How  a 

many  pounds  of  water  will  it  displace?  1  / 

(c)  What  will  be  the  buoyant  force  acting  !,' 

upon  it?/  _  <[•* 

122. '  Center    of   Buoyancy.     Let 
Fig.  99   represent   a    cross  section 
of  a  boat.    G  is  the  center  of  grav- 
ity of  the  boat  and  B  is  the  center  — b^ 
of  buoyancy.     The  center  of  buoy-  FlG  99 
ancy  of  a  floating  body  is  the  cen- 
ter of  volume  of  the  liquid  displaced.     The  point  of  intersec- 
tion of  a  vertical  line  through  B,  with  the  middle  line  ab, 


82 


HIGH   SCHOOL   PHYSICS 


through  G  at  M  is  called  the  metacenter  of  the  system ;  that  is, 
M  is  the  metacenter.  So  long  as  the  metacenter  is  above 
the  center  of  gravity  G,  the  action  of  the  two  forces  is  to 
right  the  boat;  when  the  metacenter  falls  below  G,  the  action 
of  the  two  forces  is  to  tip  the  boat  over.  In  Fig.  100  we  have 


FIG.  100 

shown  three  positions  of  the  center  of  buoyancy  with  respect 
to  the  center  of  gravity.  In  1,  G  and  B  are  in  the  same  straight 
line;  in  2,  the  metacenter  lies  above  G,  and  the  effect  of  the  two 
forces  is  to  right  the  boat;  in  3,  tne  metacenter  lies  below  G, 
and  the  effect  of  the  forces  is  to  overturn  the  boat. 

EXERCISE.    13.   Explain  why  it  is  dangerous  for  a  person  to  stand  up 
in  a  small  boat.,/ 


DENSITY  AND  SPECIFIC  GRAVITY 

123.   Density.     The  density  of  a  body  is  its  mass  per  unit 
.volume.     This  may  be  written 

,      ..  mass        m 

density  =  — -7 =  - 

volume       v 

Density  may  be  expressed  in  grams  per  cubic  centimeter  or  in 
pounds  per  cubic  foot.  For  example,  if  10  cubic  centimeters  of 
a  given  sample  of  brass  have  a  mass  of  80  grams,  its  density, 

expressed   in   metric  units,    will  be   —  =-777  =  8  grams  per 
cubic  centimeter.     Likewise,  if  2  cubic  feet  of  the  same  piece 


MECHANICS   OF  FLUIDS  83 

of  brass  have  a  mass  of  1000  pounds,  its  density  expressed  in 

English  units  will  be  —  =  -    —  =  500  pounds  per  cubic  foot. 

v          A 

The  density  of  distilled  water  at  4°  C.  in  metric  units  is  1 
gram  per  cubic  centimeter;  in  English  units,  about  62.5 
pounds  per  cubic  foot. 

124.  Specific  Gravity.  The  specific  gravity  of  a  body  is  the 
ratio  of  its  density  to  the  density  of  some  substance  taken  as  a 
standard.  For  solids  and  liquids  the  standard  is  distilled  water 
at  4°  C.;  for  gases  the  standard  is  air  or  oxygen.  Since  for 
equal  volumes  at  a  given  place  the  densities  of  two  bodies  are 
proportional  to  their  weights,  we  may  define  specific  gravity 
as  the  weight  of  a  body  divided  by  the  weight  of  an  equal  vol- 
ume of  the  standard.  Now  when  a  body  is  weighed  in  air  and 
weighed  in  water,  the  loss  of  weight,  according  to  Archimedes' 
principle,  is  exactly  equal  to  the  weight  of  the  water  displaced, 
and  therefore  we  may  write 

wt.  of  body  in  air 
op.  g.  = 


loss  of  wt.  in  water 

Example.  The  weight'  of  a  given  mass  of  brass  in  air  is  20 
pounds;  in  water,  17.5  pounds.  The  loss  of  weight  in  water 

20 
=  20  -  17.5  '=  2.5.     The  specific  gravity,  therefore,  =  —  =  8. 

A.O 

125.  Relation  of  Specific  Gravity  to  Density.  Now  specific 
gravity  is  always  numerically  equal  to  density,  when  the  latter 
is  expressed  in  grams  per  cubic  centimeter.  For  example,  to 
say  that  the  specific  gravity  of  water  is  1  is  equivalent  to  say- 
ing that  its  density  is  one  gram  per  cubic  centimeter;  and 
likewise,  to  say  that  the  specific  gravity  of  gold  is  19.3  is  equiv- 
alent to  saying  that  gold  is  19.3  times  as  heavy  as  an  equal 
volume  of  water,  which,  in  turn,  is  equivalent  to  saying  that  1 
cubic  centimeter  of  gold  weighs  19.3  grams. 

Since  the  word  density  is  rapidly  displacing  the  older  term 
specific  gravity,  and  also  since  nearly  all  modern  density  tables 


84  HIGH   SCHOOL  PHYSICS 

are  expressed  in  grams  per  cubic  centimeter,  we  shall,  in  gen- 
eral, in  this  text,  use  only  the  term  density,  meaning  thereby, 
unless  expressly  stated  to  the  contrary,  grams  per  cubic  centi- 
meter. 

EXERCISE.  14.  A  cubic  foot  of  water  weighs  62.5  Ibs.  What  is  the 
weight  of  a  cubic  foot  of  gold? 

126.  How  to  Find  the  Density  of  a  Body.     1.    If  the  body  be 
regular  in  outline,  the  most  direct  method  of  finding  its  density 
is  to  determine  its  mass  by  means  of  a  balance  and  its  volume 
by  direct  measurement.     For  example,  if  a  rectangular  block 
20  centimeters  in  length,  10  centimeters  in  width,  and  5  centi- 
meters in  height  have  a  mass  of  5  kilograms,  its  density  will 

be         m  5000 

7  =  20x10x5  =  5  gramS  per  CublC  centimeter- 

2.  If  the  body  be  irregular  in  outline  the  simplest  method 
of  finding  its  density  is  to  determine  its  specific  gravity  by 
finding  its  weight  in  air  and  then  in  water,  or  in  some  other 
fluid  chosen  as  a  standard.  As  we  wish  to  express  density  in 
metric  units,  and  since  specific  gravity  is  numerically  equal  to 
density  in  these  units,  it  follows  that  the  specific  gravity 
values  thus  obtained  will  be  equivalent  to  the  density  values  in 
grams  per  cubic  centimeter. 

EXERCISES.  15.  If  10  cc.  of  lead  have  a  mass  of  113  grams,  what  is 
its  density? 

16.  If  the  density  of  a  body  be  6  g.  per  cc.  and  its  volume  10  cc.,  what 
is  its  mass? 

17.  A  piece  of  glass  of  density  2.6  g.  per  cc.  has  a  mass  of  13  grams. 
What  is  its  volume? 

18.  A  given  piece  of  iron  weighs  225  Ibs.  in  air,  and  an  equal  volume  of 
water  weighs  30  Ibs.     Find  (a)  the  specific  gravity  of  the  iron;    (b)  its 
density. 

127.  To  Find  the  Density  of  a  Solid  Heavier  than  Water. 

If  the  body  be  of  such  a  form  that  its  volume  cannot  readily  be 
determined,  as  in  the  case  of  an  irregular  piece  of  metal,  the 


MECHANICS  OF  FLUIDS 


85 


method  of  finding  its  density  is  to  find  its  specific  gravity. 
Weigh  the  body  in  air,  then  in  water.  The  loss  of  weight  in 
water  is,  according  to  Archimedes'  principle,  the  weight  of  water 
displaced;  that  is,  the  weight  of  an  equal  volume  of  water. 
Hence  we  may  write 

wt.  in  air 
density  in  g.  per  cc.  =  Sp.  gr.  =  loss  of  wL  in 


Experiment.  Either  by  means  of  a  spring  balance,  or  a  beam 
balance,  Fig.  110,  determine  the  specific  gravity  of  an  irreg- 
ular body,  such  as  a  stone  or 
a  piece  of  metal. 

Example. 

Weight  of  body  in  air,  10  gm. 
Weight  of  body  in  water,  8  gm. 
Loss  of  weight  in  water,  2  gm. 
wt.  in  air 


D  = 


of  wt.  in  water 


10 


=  -^-  =  5  grams  per  cc. 

A 


FIG.  101 


128.  Density  of  Solids  Lighter  than  Water.  Suppose  that 
we  wish  to  find  the  density  of  a  piece  of  wood,  paraffin,  or  other 
body  lighter  than  water.  Provide  a  metal  sinker  sufficiently 
heavy  to  sink  the  given  body.  Weigh  the  sinker  in  air  and 
in  water.  Next  weigh  the  given  body  in  air,  and  then  attach 
the  sinker  and  weigh  both  in  water.  The  loss  of  weight  of  the 
sinker  and  body  minus  the  loss  of  weight  of  the  sinker  equals 
the  weight  of  a  volume  of  water  equivalent  to  the  volume  of  the 
body. 

Example.     To  find  the  density  of  a  piece  of  wood. 
Weight  of  sinker  in  air  =  33  grams 
Weight  of  sinker  in  water  =  30  grams 
Loss  of  weight  of  sinker  =  3  grams 
Weight  of  wood  in  air  =  10  grams 


86  HIGH   SCHOOL  PHYSICS 

Weight  of  wood  and  sinker  in  air  =  43  grams 

Weight  of  wood  and  sinker  in  water  =  20  grams 

Loss  of  weight  of  wood  and  sinker  =  23  grams 

Weight  of  water  displaced  by  wood  =  23  —  3  =  20  grams 

D  =  I  IF  =  0.5  gram  per  cc. 

9* 

129.  Density    of    Solids    Soluble    in    Water.     Weigh    the 
body  in  air,  then  in  some  liquid  in  which  it  does  not  dis- 
solve.    Determine  its  specific  gravity  relative  to  this  liquid. 
Multiply  the  specific  gravity  thus  obtained  by  the  density  of 
the  liquid. 

Example.  To  find  the  density  of  rock  candy.  Since  all 
forms  of  sugar  are  more  or  less  soluble  in  water,  it  will  be  neces- 
sary to  select  some  liquid  in  which  the  candy  is  not  soluble,  as 
for  example,  kerosene. 

Weight  of  candy  in  air  =  20  grams 

Weight  of  candy  in  kerosene  =10  grams 

Loss  of  weight  in  kerosene  =  20—  10  =  10  grams 

Sp.  g.  relative  to  kerosene  =  f  -{J -  =  2 

Density  of  kerosene  =  0.8  gram  per  cc. 

Density  of  candy  =  2  X  0.8  =  1.6  grams  per  cc. 

130.  Density  of  a  Liquid.     1.   Specific  gravity  bottle  method. 
A  specific  gravity  bottle  is  a  small  glass  bottle  having  a  per- 
forated glass  stopper,  Fig.   102.     First  determine 
the  weight  of  the  empty  bottle.     Next  weigh  the 
bottle  filled  with  distilled  water.     The  difference 
between  these  two  weights  is  the  weight  of  a  given 
volume   of  water.     Now   fill  the   bottle  with  the 
liquid  whose  specific  gravity  is  to  be  found,  and 
weigh   as   before.     Again   subtracting  the   weight 
of    the    bottle    gives    the    weight    of    the    liquid. 

This  weight  divided  by  the  weight  of  the  water  is  the  specific 
gravity. 


MECHANICS  OF   FLUIDS 


87 


Example.     To  find  the  density  of  glycerine. 
Weight  of  bottle  =  15  grams 
Weight  of  bottle  filled  with  water  =  65  grams 
Weight  of  bottle  filled  with  glycerine  =  78  grams 


D  = 


78-15       63 

-£=  -  1-=-  =  FT;  =  1.26  grams  per  cc. 

oo  —  lo       oU 


2.  Density  of  a  liquid  by  the  sinker  method.    Weigh  a  sinker 
in  air;   then  weigh  the  same  sinker  in  the  given  liquid;   finally 
weigh  the  sinker  in  water.    Now  since  the  sinker  displaces  equal 
volumes  of  both  the  given  liquid  and  of  water,  it  follows  that  the 
ratio  of  the  loss  of  weight  in  each  case  is  the  specific  gravity. 

Example.     Density  of  alcohol  by  the  sinker  method. 
Weight  of  sinker  in  air  =  20  grams 
Weight  of  sinker  in  alcohol  =  18.36  grams 
Loss  of  weight  in  alcohol  =  1.64  grams 
Weight  of  sinker  in  water  =18  grams 
Loss  of  weight  in  water  =  2  grams 

1.64 
D  =    '      =  0.82  gram  per  cc. 

z 

3.  Density  of  a  liquid  by  the  hydrometer  method.     A  hy- 
drometer is  a  device  for  determining  the  density 

of  a  liquid  by  immersing  the  instrument  in  the 
liquid.  Experiment.  If  a  hydrometer  be  placed 
in  a  jar  of  water,  Fig.  103,  the  instrument  will 
float  in  a  vertical  position,  displacing  a  certain 
amount  of  the  liquid.  Now  if  the  hydrometer 
be  placed  in  another  liquid  of  greater  density, 
such  as  a  strong  solution  of  salt  and  water,  it 
will  float  at  a  different  level.  If  the  instrument 
be  properly  calibrated,  it  will  be  possible  to  de- 
termine the  density  of  the  salt  solution  directly 
from  the  scale.  It  is  evident  that  a  hydrom- 
eter with  a  scale  suitable  for  heavy  liquids 
will  not  do  for  light  liquids,  because  the  instru-  FIG.  103 


88  HIGH  SCHOOL  PHYSICS 

ment  in  the  latter  case  would  sink  to  the  bottom.  Hydrom- 
eters, therefore,  are  calibrated  with  reference  to  the  use  to 
which  they  are  to  be  put.  A  hydrometer  calibrated  to  give 
the  density  of  milk  is  called  a  lactometer;  to  give  the  density  of 
syrup,  a  saccharimeter;  the  density  of  acids,  an  acidimeter,  etc. 

EXERCISES.  19.  A  piece  of  metal  weighs  16  grams  in  air  and  14  grams 
in  water.  What  is  its  density? 

20.  A  stone  having  a  mass  of  20  grams  is  dropped  into  a  beaker  which 
is  "level  full"  of  water,  causing  5  cc.  of  water  to  flow  out.     Find  the  density 
of  the  stone. 

21.  A  piece  of  paraffin,  which  is  lighter  than  water,  weighs  18  grams  in 
air.     There  is  attached  to  the  paraffin  a  sinker  which  weighs  40  grams  in 
air  and  35  grams  in  water.     The  sinker  and  paraffin  together  weigh  33 
grams  in  water.     Find  the  density  of  the  paraffin. 

22.  A  sinker  weighs  25  grams  in  air  and  20  grams  in  water.     Find  the 
density  of  a  liquid  in  which  it  weighs  (a)  23  grams;    (b)  19  grams. 

23.  A  specific  gravity  bottle  when  empty  weighs  30  grams.     When 
filled  with  water  it  weighs  70  grams;    when  filled  with  oil  it  weighs  60 
grams.     Find  the  density  of  the  oil. 

PRESSURE  DUE  TO  GASES 

131.  The  Atmosphere.  The  air  composing  the  atmosphere 
consists  mainly  of  two  gases,  oxygen  and  nitrogen,  in  the  ratio 
by  volume  of  one  part  0  to  four  parts  N.  These  gases  exist  in 
the  air  as  a  mechanical  mixture.  The  most  important  physical 
properties  of  the  air  are  as  follows:  (a)  Air  like  all  fluids  is 
perfectly  elastic;  (b)  it  is  highly  compressible,  as  illustrated 
daily  in  the  compression  of  air  in  the  pumping  up  of  bicycle 
and  automobile  tires.  Due  to  this  property  of  compressibility, 
most  of  the  atmosphere  lies  very  near  the  surface  of  the  earth. 
At  a  height  of  3  miles,  altitude  of  Mt.  Blanc,  Fig.  104,  the 
density  of  the  air  is  only  one-half  that  at  sea  level.  Men 
have  ascended  in  balloons  to  a  height  of  about  7  miles, 
at  which  altitude  the  density  was  found  to  be  about  one- 
fourth  that  at  sea  level.  By  means  of  automatic  barometers 
sent  up  in  balloons,  it  has  been  possible  to  explore  the  atmos- 


MECHANICS  OF   FLUIDS 


89 


phere  to  a  height  of  some  18  miles.  It  is  estimated  that  at  a 
height  of  35  miles  the  density  of  the  atmosphere  is  only  about 
30/000  of  that  at  the  earth's  surface.  How  far  beyond  this 
the  rarefied  atmosphere  extends  is  not  definitely  known,  the 
distance  being  variously  esti- 
mated at  from  100  to  500  miles. 

132.  Air  Has  Weight.  Ex- 
periment. Exhaust  the  air  from 
a  hollow  globe  by  means  of  an 
air  pump.  Suspend  this  globe 
from  the  arm  of  a  beam  balance 
and  counterpoise,  Fig.  105.  Now 
while  the  balance  is  in  equilib- 
rium, open  the  stop  cock,  ad- 
mitting air  into  the  globe.  It 
will  be  found  that  the  globe 
will  appear  heavier  than  before, 
the  balance  being  out  of  equilib- 
rium, as  shown  in  Fig.  106.  The 
globe  when  filled  with  air  weighs 
more  than  when  empty. 

The  mass  of  a  unit  volume  of 
air  depends  upon  the  density  of 


FIG.  104 
Density  of  Atmosphere 


the  atmosphere,  which  varies  from  day  to  day  and  from  point 
to  point  on  the  earth's  surface.     Under  standard  conditions, 


A 


FIG.  105 


FIG.  106 


that  is  at  sea  level,  and  at  a  temperature  of  0°  C.  (the  freez- 
ing point  of  water),  the  mass  of  1  cubic  centimeter  of  air  is 
0.00129  gram;  the  mass  of  1  cubic  foot,  0.08  pound. 


90 


HIGH   SCHOOL   PHYSICS 


133.  Rise  of  Liquids  in  Tubes.  Everyone  is  familiar  nowa- 
days with  the  method  of  drinking  lemonade  and  sodas  by  suc- 
tion through  a  tube.  Of  course  it  is  generally  known  that  by 
" suction"  we  mean  the  exhaustion  of  the  air  within  the  tube, 
thus  alfowing  the  pressure  of  the  atmosphere  to  force  the 
liquid  upward.  The  fact  that  a  liquid  is  not  drawn  up  by  suc- 
tion, but  is  forced  up  by  atmospheric  pressure,  was  not  always 
known,  however,  as  is  illustrated  by  the  story  of  the  Duke  of 
Tuscany 's  pump.  In  the  days  of  Galileo  the  phenomenon 
of  suction,  so  called,  was  explained  by  saying  that  "  nature 
abhorred  a  vacuum."  It  is  related  that  the  Duke  of  Tuscany, 
of  Florence,  Italy,  1640,  had  a  deep  well  dug  on  his  estate, 
and  found,  much  to  his  surprise,  that  the 
water  would  not  rise  in  the  pump  to  a 
height  of  more  than  about  30  feet.  This 
was  a  case,  as  Galileo  put  it,  in  which  nature 
seemed  to  abhor  a  vacuum  only  to  the 
height  of  32  feet.  Torricelli,  a  young  Ital- 
ian scientist  and  pupil  of  Galileo,  undertook 
to  solve  the  problem  of  the  mysterious 
behavior  of  the  water  in  the  Duke's  deep 
well  pump. 

134.  Torricelli's  Experiment.  Torricelli 
conceived  the  idea  that  the  reason  the  water 
did  not  rise  to  a  height  greater  than  32  feet 
was  due  to  the  fact  that  the  pressure  of  the 
atmosphere  was  not  great  enough  to  sup- 
port a  column  of  water  beyond  this  point. 
He  used  for  his  purpose  a  column  of  mer- 
cury, which,  being  13.6  times  as  heavy  as 
water,  enabled  him  to  use  a  tube  of  con- 
venient length.  His  experiment  may  be 
performed  as  follows:  A  glass  tube  about  80  centimeters  in 
length  and  closed  at  one  end  is  filled  with  mercury,  Fig.  107. 
The  open  end  is  closed  with  the  finger  and  the  tube  inverted; 


FIG.  107 


MECHANICS  OF  FLUIDS 


91 


the  temporarily  closed  end  is  then  placed  under  mercury  in 
the  dish  and  the  finger  removed.  The  mercury  in  the  tube 
falls  until  the  pressure  due  to  the  column  AB  is  just  sufficient 
to  counterbalance  the  pressure  of  the  air  acting  upon  the  sur- 
face of  the  mercury  in  the  dish.  At  sea  level  the  column  AB 
is  about  30  inches,  or  76  centimeters  in  height.  The  space 
above  the  mercury  in  the  tube  is  called  a  Torricellian  vacuum ; 
it  contains  a  small  amount  of  mercury  vapor. 

Torricelli  concluded  from  this  experiment  that  air  has  weight 
and  exerts  pressure,  and  he  thus  explained  the  rise  of  liquids  in 
tubes  from  which  the  air  has  been  exhausted.  This  experi- 
ment also  demonstrated  in  a  satisfactory  manner  that  the 
failure  of  the  water  to  rise  to  the  surface  in  a  deep  well  pump 
was  not  due  to  the  presence  of  an  evil  spirit,  as  was  thought, 
but  is  due  to  the  fact  that  the  pressure  of  the  atmosphere 
is  sufficient  to  support  a  column  of  water  not  greater  than  32 
feet  in  height. 

135.  Air  Pressure  Experiments.  Experiment  1.  Atmos- 
pheric pressure  may  be  strikingly  illustrated  by  the  tumbler 
experiment,  Fig.  108.  In  this  case  a  tumbler  of  water  having  a 
sheet  of  paper  pressed  firmly  over  the  mouth  is  inverted.  The 
water  and  paper  are  held  in  position  by  atmospheric  pressure. 


FIG.  108 


FIG.  109 


FIG.  110 


Experiment  2.  The  device  shown  in  Fig.  109,  consisting  of  a 
funnel,  a  glass  plate,  and  a  number  of  metal  weights,  illustrates 
the  principle  of  air  pressure  in  a  manner  even  more  striking 


92 


HIGH   SCHOOL   PHYSICS 


than  that  of  the  tumbler  experiment.  The  funnel  is  inverted 
over  the  weights,  which  are  piled  upon  a  glass  plate,  and  the 
air  exhausted  through  the  rubber  tube  by  suction  (Supplement, 
554) .  Again  the  atmospheric  pressure  manifests  itself  in  sup- 
porting the  plate  with  the  weights  upon  it. 

Experiment  3.  The  experiment  with  Magdeburg  hemi- 
spheres (Supplement,  554)  is  one  of  the  classics  of  experimental 
physics.  The  two  hollow  hemispheres,  Fig.  110,  are  fitted 
together^and  the  air  exhausted  by  means  of  an  air  pump.  The 
force  holding  the  air  together  is  equal  to  a  pressure  of  14.7 
pounds  per  square  inch  of  cross  sectional  area  of  the 
sphere  through  the  center. 

136.  The  Barometer.  The  mercury  barometer  is  a 
Torricellian  tube  fastened  to  a  frame  having  a  scale, 
by  means  of  which  the  height  of  the  mercury  may  be 
read,  Fig.  111.  If  such  a  barometer  be  carried  up  a 
mountain  side  the  mercurial  column  will  fall,  due  to 
the  diminished  pressure  of  the  atmosphere;  if  it  be 
taken  down  into  a  deep  mine 
or  a  valley  the  mercurial  col- 
umn will  rise. 

The  aneroid  barometer  con- 
sists of  a  metallic  box  from 
which  a  part  of  the  air  has 
been  exhausted,  Fig.  112. 
Variations  Of  atmospheric 
pressure  affect  the  outer  case 
of  the  instrument,  which  in 
turn  acts  upon  a  system  of 
levers  connected  to  the  point- 
ers. One  of  these  pointers 


Fig.  Ill 


FIG.  112 
Aneroid  Barometer 


indicates  changes  of  atmospheric  pressure,  the  other  indicates 
probable  changes  of  the  weather,  as  Fair,  Change,  etc.  The 
advantage  of  an  aneroid  barometer  lies  in  the  fact  that  it  is 
small  and  is  therefore  easily  handled.  It  is  not  so  reliable, 


MECHANICS  OF  FLUIDS 


93 


however,  as  a  mercury   barometer,  because   the   mechanical 
parts  of  the  apparatus  are  likely  to  get  out  of  adjustment. 

137.  Pressure    of    One    Atmosphere.     The    expression    "a 
pressure  of  one  atmosphere"  means  the  pressure  exerted  by 
the  atmosphere  at  sea  level  and  at  0°  C.  (the  freezing  point  of 
water).     Under  standard  conditions  (sea  level  and  0°  C.)  the 
height  of  the  barometric  column  is  76  centimeters,  which  is 
equivalent  to  about  30  inches.     A  column  of  mercury  76  cen- 
timeters in  height  and  having  a  cross  sectional  area  of  1  square 
centimeter  has  a  mass  of  1033.3  grams.     A  pressure  of  one 
atmosphere,  therefore,  is  equal  to  1033.3  grams  per  square  cen- 
timeter, which  is  equivalent  to  14.7  pounds  per  square  inch. 

One  atmosphere  =  76  centimeters  of  mercury  =  30  inches  of 
mercury  =  1033.3  grams  per  square  centimeter  =14.7  pounds 
per  square  inch. 

138.  Use  of  the  Barometer  as  a  Weather  Indicator.     Con- 
stant use  is  made  of  the  barometer  by  the  Weather  Bureau 
in  forecasting  changes  in 


the  weather.  The  rela- 
tion between  barometric 
readings  and  the  direc- 
tion of  the  wind  may 
be  studied  in  connection 
with  the  weather  map. 
A  portion  of  such  a  map 
used  by  the  United  States 
Weather  Bureau  is  shown 
in  Fig.  113.  The  heavy 
curved  lines,  called  iso- 
bars, are  lines  passing 
through  places  of  equal 

atmospheric  pressure.  At  the  place  marked  LOW  the  atmos- 
pheric pressure  is  least;  while  at  the  place  marked  HIGH  the 
pressure  is  greatest.  The  air  flows  into  this  "low"  region, 
forming  a  sort  of  whirlpool.  In  the  northern  hemisphere 


FIG.  113 


94  HIGH   SCHOOL   PHYSICS 

winds  are  deflected  to  the  right  by  the  rotation  of  the  earth; 
hence  in  the  United  States  the  general  direction  of  the  wind 
about  these  areas  of  low  pressure  is  counter-clockwise;  that 
is,  in  the  opposite  direction  to  the  hands  of  a  clock.  If  a 
person  stand  with  his  back  to  the  wind,  the  storm  center,  that 
is  the  region  of  low  barometric  pressure,  will  in  general  be 
on  his  left  hand.  The  observations  of  the  Weather  Bureau 
on  barometric  pressure  for  a  series  of  years  indicate  that  these 
low  pressure  areas  are  continually  passing  over  the  country 
with  considerable  regularity  and  along  pretty  well  denned 
paths.  The  forecaster  depends  largely  upon  his  knowledge 
of  the  movements  of  these  areas  in  predicting  the  weather. 

The  relation  of  the  barometric  reading  to  the  probable  con- 
dition of  the  weather  may  be  stated  as  follows:  (a)  A  rising 
barometer  precedes  fair  weather;  (b)  a  falling  barometer  pre- 
cedes foul  weather;  (c)  a  sudden  fall  in  the  barometer  indi- 
cates a  storm;  (d)  a  steady  barometer  indicates  settled  fair 
weather. 

139.  Boyle's  Law.  If  a  gas  be  confined  in  a  vessel,  Fig.  114, 
and  pressure  be  applied  to  the  piston,  the  volume  of  gas  will  be 
diminished  and  its  density  increased.  An  increase  of 
pressure,  then,  produces  a  decrease  in  volume,  if  the 
temperature  be  constant.  The  relation  betwreen  the 
volume  of  a  gas  and  the  pressure  to  which  it  is  sub- 
jected was  first  investigated  by  Boyle.  (1627-1691.) 
The  results  obtained  were  formulated  in  what  is 
commonly  known  as  Boyle's  law :  The  temperature 
remaining  constant,  the  volume  of  a  gas  varies  inversely 
as  the  pressure. 

Since  the  volume  decreases  in  the  same  ratio  as  the  pressure 
increases,  this  law  is  sometimes  written  in  the  form  of  an 
equation : 

pv  =  c 
in  which  C  is  a  constant,  as  explained  in  the  next  topic. 


MECHANICS  OF  FLUIDS 


95 


140.  Verification  of  Boyle's  Law.  Boyle's  law  and  its  equa- 
tion may  be  verified  by  means  of  an  apparatus  similar  to  that 
shown  in  Fig.  115.  To  begin  with,  the  mercury  stands  at  the 
same  level  in  both  parts  of  the  apparatus.  The  air 
in  the  chamber  C,  20  cubic  centimeters  say,  is  under  a 
pressure  of  one  atmosphere.  Now,  applying  the  law, 
we  have 

pv  =  1  X  20  =  20. 


Now  suppose  that  the  vessel  V  be  elevated  as  shown 
in  Fig.  115,  until  the  pressure  upon  the  enclosed  air  is 
2  atmospheres.     The  volume   is  now  10  centimeters 
and  the  pressure  is  2  atmospheres.     Since 
we  have  a  different  pressure  and  a  differ- 
ent  volume    to    deal    with,   the    law    is     |«|C 
written 

pV  =  2  X  10  =  20. 

If  the  pressure  were  increased  to  4  at- 
mospheres the  volume  would  be  decreased 
to  5  cubic  centimeters;  hence  FlG  115 

p'V  =  4  X  5  =  20. 

It  will  be  noted  that  in  every  case  the  product  of  the  pres- 
sure times  the  volume  is  the  same;  in  other  words,  the  product 
of  pressure  and  volume  is  a  constant ;  that  is,  pv  =  c. 

141.  Boyle's  Law  Approximate.  Investigation  has  shown 
that  Boyle's  law  is  only  approximately  true  for  all  gases.  For 
example,  those  gases  which  are  easily  liquefied,  such  as  carbon 
dioxide  (CO2),  sulphur  dioxide  (S02),  and  chlorine  (Cl),  show 
the  greatest  variation  from  the  law.  Within  moderate  limits 
of  pressure,  however,  Boyle's  law  is  exceedingly  useful  in  the 
study  of  gases. 


96 


HIGH   SCHOOL  PHYSICS 


id 


C| 


APPLICATIONS  OF  AIR  PRESSURE 

142.  The  Siphon.     The  siphon  is  a  device  for  transferring 
liquids  from  a  given  level  to  a  lower  level  over  an  intervening 
elevation.     It  depends  for  its  operation  on  atmospheric  pres- 
sure.    Fig.  116  shows  a  siphon  in  operation.     The  arm  in  the 
vessel  from  which  the  liquid  flows  is 

called  the  short  arm;  it  is  measured 
from  the  surface  of  the  liquid  to  the 
highest  point  in  the  bend  of  the  tube, 
ab.  The  other  arm  is  called  the  long 
arm,  ce.  In  case  the  long  arm  dip 
into  the  liquid,  its  length  is  measured 
from  c  to  the  surface  of  the  liquid. 

Experiment.  The  effect  of  increas- 
ing the  long  arm  is  to  increase  the 
rate  of  flow.  When  the  two  arms  are 
of  the  same  length  the  flow  ceases; 
the  liquid  remains  stationary  in  the 
tube.  When  the  outer  arm  is  made  shorter  than  the  inner  arm, 
the  liquid  in  the  tube  will  flow  back  into  the  vessel. 

143.  Action  of  the  Siphon.     Let  P  be  the  downward  pres- 
sure of  the  atmosphere  on  the  surface  of  the  liquid.     Since, 
according  to  Pascal's  law,  pressure  is  transmitted  equally  in 
all  directions  throughout  the  liquid,  P  is  therefore  the  upward 
pressure  on  the  liquid  in  the  short  arm  ab.     Let  p  be  the  pres- 
sure due  to  the  weight  of  the  water  in  this  arm.     The  effective 
upward  pressure,  then,  on  the  short  arm  is  P  —  p.     Likewise, 
the  upward  pressure  due  to  the  atmosphere  on  the  long  arm  cde 
is  also  P,  the  slight  difference  in  pressure  due  to  the  difference 
in  level  of  the  two  arms  being  negligible.     This  means  that  the 
upward  pressure  due  to  the  atmosphere  is  practically  the  same 
on  both  arms.     Now  suppose  that  the  pressure  due  to  the  weight 
of  the  liquid  in  the  long  arm  cde  be  p',  then  the  effective  upward 
pressure  on  this  arm  is  P  —  p'.    Since  there  is  more  water  in 


FIG.  116 


MECHANICS  OF   FLUIDS 


97 


the  long  arm  than  in  the  short  arm,  p'  is  greater  than  p;  hence 
it  follows  that  P  —  p  is  greater  than  P  —  p';  that  is,  the  greater 
upward  force  acts  on  the  short  arm,  and  hence  the  liquid  flows 
towards  the  long  arm. 

144.  The  Intermittent  Siphon.  Experiment.  Seal  a  bent 
glass  tube  into  a  funnel,  as  shown  in  Fig.  117.  Pour  water 
slowly  into  the  vessel.  When  it  rises  to  the  top  of  the  tube  a 
the  siphon  begins  to  operate,  and  continues  to  flow  until  the 
water  falls  below  the  opening  at  6.  The  siphon  ceases  to  flow 
until  the  water  is  again  above  a,  when  it  starts  again.  Because 
of  the  character  of  the  flow,  such  a  device  is  known  as  an 
intermittent  siphon. 


=c /-a 


FIG.  118 


EXERCISES.    24.   Will  a  siphon  work  in  a  vacuum?     Why? 

25.  Explain  (a)  why  the  flow  ceases  when  the  two  arms  of  a  siphon  are 
of  the  same  length;    (b)  why  the  liquid  flows  back  into  the  vessel  when 
the  outer  arm  is  shorter  than  the  inner  arm. 

26.  Sulphuric  acid  has  a  density  of  1.84,  that  is,  it  is  1.84  times  as 
heavy  as  water,     (a)  Over  what  height  can  it  be  siphoned?     (b)  Over 
what  height  can  kerosene  (density  0.8)  be  siphoned?     (c)  Mercury  (den- 
sity 13.6)? 

27.  Explain  the  operation  of  the  intermittent  spring,  Fig.  118. 

145.  The  Lift  Pump.  Fig.  119  shows  a  section  of  a  common 
cistern  pump.  The  principle  upon  which  it  works  is  illustrated 
by  diagrams  A  and  B  of  Fig.  120.  The  pump  contains  two 
valves  v  and  vf,  both  of  which  open  upward.  Diagram  A  illus- 
trates the  operation  of  the  valve  during  a  downward  stroke  of 


98 


HIGH   SCHOOL  PHYSICS 


the  piston;  B  shows  the  condition  of  the  valve  during  the 
upward  stroke.  When  the  pump  is  first  operated,  the  action 
of  the  piston  and  valves  exhausts  the  air  from  the  chamber  C. 
During  this  stage  it  acts  as  an  air  pump.  The  atmospheric 
pressure  upon  the  surface  of  the  water  in  the  well  forces  the  water 
up  into  the  pump  until  both  valves  become  submerged,  Fig.  119. 
As  the  pump  continues  to  operate  the  valves  act  exactly  as 
explained  in  diagrams  A  and  B,  Fig.  120. 


A 


FIG.  119 


FIG.  120 


FIG. 


146.  The  Deep  Well  Pump.  Since  the  pressure 
of  the  atmosphere  is  capable  of  supporting  a  column 
of  water  only  about  30  feet  in  height,  a  pump  hav- 
ing  valves  near  the  surface,  as  in  the  case  of  the 
ordinary  cistern  pump,  would  be  of  no  value  in  lifting  water 
from  a  well  more  than  about  30  feet  deep.  To  make  a  deep 
well  pump  effective  it  is  necessary  to  place  both  valves  near 
the  water.  In  the  case  of  the  deep  well,  such  as  the  drive 
well  for  example,  the  valves  are  usually  placed  within  a  few 
feet  of  the  water,  Fig.  121. 


MECHANICS  OF   FLUIDS 


99 


147.  The  Force  Pump.  A  force  pump  serves  both  to  lift 
water  from  the  well  and  also  to  deliver  it  in  a  steady  stream 
under  pressure.  In  the  force  pump  there  is  no  valve  hi  the 
plunger,  Fig.  122.  The  chamber  C  is  partly  filled  with  air. 
When  water  is  forced  into  this  chamber  by  the  downward  stroke 
of  the  plunger  P,  the  air  is  compressed;  during  the  upward 
stroke  of  P,  valve  v  is  closed  and  the  air  cushion  expands, 
forcing  the  water  through  the  delivery  pipe  in  a  steady  stream. 


n 


FIG.  122 


FIG.  123 


148.  The  Air  Pump.  An  air  pump  does  not  differ  in  prin- 
ciple from  that  of  the  water  pump.  The  simple  exhaust  pump 
is  shown  in  Fig.  123.  On  the  downward  stroke  of  the  piston, 
valve  v  opens,  allowing  the  air  in  chamber  C  to  escape. 
On  the  upward  stroke  of  the  piston,  air  is  drawn  from  the 
receiver  R. 

The  pump  shown  in  this  figure  would  not  be  very  effective, 
however,  because  the  degree  of  exhaustion  obtained  would  be 
limited  to  the  pressure  required  to  lift  valve  v'.  The  modern 
air  pump  is,  therefore,  provided  with  metallic  valves  which  are 
ground  so  as  to  fit  very  accurately  and  which  are  operated  by 
the  mechanical  action  of  the  piston.  (Supplement,  555.) 

149.  The  Condensing  Pump.  If  the  valves  of  an  air  pump 
be  reversed  and  operated  as  in  Fig.  124,  air  will  be  forced  into 
the  receiver  R.  Such  a  pump  is  called  a  condensing  pump. 


100 


HIGH  SCHOOL  PHYSICS 


The  common  bicycle  pump  is  one  of  the  simplest  types  of  a 
condensing  pump.  One  valve  is  connected  with  the  bicycle 
tire  and  the  other  forms  part  of  the  piston  of  the  pump,  Fig. 


FIG.  124 


FIG.  125 


125.  On  the  upward  stroke  of  the  piston  P,  valve  s  in  the  tire 
closes,  and  the  cup-shaped  piece  of  leather  c  allows  the  air  to 
pass  down  into  the  chamber  C.  On  the  downward  stroke  of  P 
the  air  is  driven  into  the  tire. 

Compressed  air  is  very  extensively  employed  today  in  operat- 
ing drills,  riveting  hammers,  and  automatic  air  brakes  such  as 
are  used  on  modern  electric  and  steam  cars.  Compressed  air 
is  also  used  in  the  diving  bell,  a  device  which  enables  workmen 
to  operate  under  water.  (Supplement,  556.) 

150.  The  Mercury  Air  Pump.  A  very  good  mechanical 
pump  will  exhaust  a  vessel  till  the  pressure  of  the  remaining  air 
in  the  receiver  will  support  a  column  of  mercury  of  less  than  one 
millimeter  in  height.  In  order  to  get  a  better  vacuum  than  this 
it  is  necessary  to  use  some  form  of  the  so-called  mercury  air 
pump.  These  pumps  are  usually  made  of  glass,  mercury  play- 
ing a  part  somewhat  analogous  to  that  of  the  piston  in  the 
mechanical  air  pump.  The  principle  upon  which  the  mercury 
pump  operates  is  shown  in  Fig.  126.  A  column  of  mercury  is 
allowed  to  fall  through  a  long  tube.  In  passing  through  cham- 
ber C  it  breaks  up  into  drops  each  of  which  serves  as  a  piston 
to  carry  a  portion  of  the  air  downward,  thus  exhausting  the  air 


MECHANICS   OF 


'.  '•  101 


from  C.  As  the  pressure  within  the  receiver  is  reduced  it  is 
obvious  that  the  mercury  will  rise  in  the  tube  B,  standing  at 
a  height  of  76  centimeters  when  the  exhaustion  is  complete. 

Pumps  of  this  type  are  often  used  in  exhausting 

the  air  from  electric  light  bulbs. 

The   most   modern  type  of   mercury   air  pump 

will   produce   a   vacuum   of    one   millionth   of   an 

atmosphere. 

151.   The  Water  Jet  Pump.    The  water  jet  pump, 

or  aspirator,  Fig.  127,  is  a  form  of  pump  adapted 

for  use  where  water  under  high  pressure  is  available, 


D 


FIG.  126 


FIG.  127 


FIG.  128 


as  from  the  city  water  supply.  A  stream  of  water  under 
pressure  enters  the  tube  a,  which  is  constricted  at  the  lower 
end,  thus  giving  a  high  velocity  at  b.  The  air  is  drawn  along 
with  the  stream  of  water  in  the  form  of  small  bubbles,  thus 
exhausting  the  chamber  C.  With  a  pump  of  this  kind  it  is 
possible,  with  the  water  from  the  city  mains,  to  obtain  a  vac- 
uum of  about  5  centimeters  of  mercury. 

EXERCISE.  28.  A  pressure  of  one  atmosphere  is  equivalent  to  a  column 
of  mercury  76  cm.  in  height.  What  atmospheric  pressure  is  represented 
by  a  pressure  equivalent  to  5  cm.  of  mercury? 

152.  The  Ejector.  If  a  strong  current  of  air  be  blown  across 
the  opening  of  a  tube,  Fig.  128,  the  air  in  the  upper  part  of  the 
tube  will  be  dragged  out  by  the  moving  column  and  pressure 


1.02 


HIGH   SCHOOL   PHYSICS 


within  thus  reduced.  If  the  lower  end  of  the  tube  be  immersed 
in  a  liquid  to  which  the  atmosphere  has  free  access,  the  liquid 
will  be  forced  to  the  mouth  of  the  tube,  where  it  is  blown  into  a 
fine  spray.  Such  an  instrument  is  called  an  ejector.  It  explains 
the  principle  upon  which  the  atomizer  works, 
also  the  principle  employed  in  the  apparatus 
used  so  commonly  for  the  spraying  of  trees  and 
shrubs. 

When  a  strong  wind  is  blowing  across  the  top 
of  the  chimney,  Fig.  129,  this  ejector  principle 
comes  into  play,  and  a  strong  upward  draft  is 
created  in  the  chimney. 

153.  Buoyancy  of  the  Air.  According  to 
Archimedes'  principle,  bodies  immersed  in  a  fluid  are  buoyed 
up  by  a  force  equal  to  the  weight  of  the  fluid  displaced.  Now 
air  is  a  fluid  and  it  also  possesses  weight;  hence  all  bodies  in 
air  are  buoyed  up  by  the  weight  of  the  air  displaced.  The 


FIG.  130 

true  weight  of  a  body  is  its  weight  in  a  vacuum;  therefore  in 
many  accurate  scientific  measurements  of  mass  it  is  necessary 
to  reduce  the  values  obtained  in  air  to  those  corresponding 
to  a  vacuum. 

There  is  an  old  saying  that  a  pound  of  feathers  is  heavier 


MECHANICS   OF  FLUIDS  103 

than  a  pound  of  lead,  when  weighed  in  air.  This  is  in  a  sense 
true,  because  of  the  buoyancy  of  the  air,  as  can  be  shown  by  the 
following  experiment:  Counterbalance  in  air  a  hollow  spheri- 
cal vessel  against  a  small  metal  sphere,  Fig.  130.  Of  course  the 
buoyancy  of  air  upon  the  large  sphere  is  greater  than  that  upon 
the  small  sphere.  Now  place  the  balance  under  the  receiver 
of  an  air  pump  and  exhaust.  As  soon  as  the  air  is  withdrawn 
from  the  receiver  and  its  buoyant  effects  removed,  the  balance 
is  no  longer  in  equilibrium,  the  larger  sphere  now  overbalancing 
the  smaller  one.  Thus  the  two  bodies  which  apparently  had 
equal  masses  in  air  are  found  to  have  different  masses  in  a 
vacuum.  The  large  hollow  sphere  corresponds  to  the  pound 
of  feathers  and  the  small  solid  sphere  to  the  pound  of  lead. 

154.  The  Principle  of  Buoyancy  Applied  to  the  Balloon.  A 
balloon  is  an  air-tight  bag,  usually  made  of  silk,  filled  with 
a  gas  lighter  than  air,  Fig.  131.  The  buoy- 
ant force  tending  to  elevate  it  is  equal  to 
the  weight  of  air  which  it  displaces.  The 
gas  generally  used  for  inflating  balloons  is 
either  hydrogen  or  illuminating  gas,  usually 
the  latter,  on  account  of  its  comparative 
cheapness.  Under  standard  conditions  a 
cubic  foot  of  hydrogen  has  a  mass  of  about 
0.006  pound;  a  cubic  foot  of  illuminating 
gas,  0.05  pound;  a  cubic  foot  of  air,  0.08 
pound.  Now  in  order  to  compare  the  net 
buoyant  effect  acting  upon  equal  volumes 
of  two  of  these  gases,  we  shall  consider  the 
following  example :  Given  two  toy  balloons  of  the  same  volume, 
one  containing  a  cubic  foot  of  hydrogen  and  the  other  a  cubic 
foot  of  illuminating  gas,  to  find  the  net  buoyant  effect  on  each. 
Solution :  The  weight  of  air  displaced  by  each  balloon  is  the 
same;  namely,  0.08  pound.  The  net  buoyant  effect  in  each 
case  will  therefore  be  the  difference  between  the  weight  of 
air  displaced  and  the  weight  of  the  balloon;  that  is,  for 


104  HIGH  SCHOOL  PHYSICS 

hydrogen  the  net  buoyant  effect  will  be  0.08  -  0.006  =  0.074 
pound  per  cubic  foot;  (b)  for  illuminating  gas,  0.08  —  0.05 
=  0.03  pound  per  cubic  foot.  Thus  we  see  that  the  net  buoy- 
ant force  acting  upon  the  hydrogen  balloon  is  about  2.5  times 
as  great  as  that  acting  upon  a  balloon  containing  illuminating 
gas. 

Dirigible  Balloon  and  Aeroplane,  Supplement,   557. 

EXERCISES  AND  PROBLEMS  FOR  REVIEW 

1.  State  and  illustrate  Pascal's  law. 

2.  A  tube  having  a  cross  section  of  2  sq.  in.  is  fitted  into  the  top  of  a 
cask,  such  as  shown  in  Fig.  81,  which  has  a  total  area  of  10  sq.  ft.     The 
cask  and  tube  are  filled  with  water.     The  force  exerted  by  the  water  in 
the  tube  is  10  Ibs.     Find  the  total  force  exerted  on  the  interior  surface  of 
the  cask. 

3.  The  diameter  of  a  small  piston  of  a  hydrostatic  press  is  1  in. ;   the 
diameter  of  the  large  piston,  1  ft.     (a)  What  is  the  ratio  of  the  area  of  the 
two  pistons?     (b)  A  force  of  10  Ibs.  on  the  small  piston  will  exert  what 
upward  force  on  the  large  piston? 

'   4.   Give  the  use  of  the  following  equation,  and  explain  meaning  of 
each  term:    F  =  AHD. 

5.  A  rectangular  vessel,  height  10  cm.,  width  20  cm.,  length  30  cm., 
is  filled  with  water.     Find  (a)  the  force  exerted  on  the  bottom;    (b)  the 
total  force  exerted  on  the  four  sides. 

6.  A  cylindrical  vessel,  radius  10  cm.,  height  20  cm.,  is  filled  with 
water.     Find  (a)  the  force  exerted  on  the  bottom;    (b)  the  force  exerted 
on  the  side. 

7.  A  cylindrical  tank  of  radius  5  ft.,  height  20  ft.,  is  filled  with  water. 
Find  (a)  the  force  exerted  on  the  bottom;  (b)  the  force  exerted  on  the 
side. 

8.  State  and  illustrate  Archimedes'  principle. 

9.  A  given  substance  having  a  volume  of  10  cc.  has  a  mass  of  15 
grams,     (a)  How  many  grams  of  water  will  it  displace  when  submerged? 
(b)  Will  it  sink  or  float,  and  why? 

10.  A  cubic  foot  of  a  given  substance  weighing  50  Ibs.  is  thrust  under 
water,     (a)  What  weight  of  water  does  it  displace?     (b)  What  is  the 
buoyant  force  acting  upon  it?     (c)  What  force  must  be  exerted  upon  it  in 
order  to  keep  it  under  water? 

11.  A  rectangular  piece  of  aluminum,  2x4x5  cm.,  has  a  density  of 
2.6  g.  per  cc.     Find  its  mass. 


MECHANICS  OF  FLUIDS  105 

12.  A  metallic  cylinder  having  a  radius  of  2  cm.  and  a  height  of  5  cm. 
has  a  mass  of  628.32  grams.     Find  its  density. 

13.  A  sphere  having  a  radius  of  2  cm.  has  a  mass  of  150  grams.     Find 
its  density. 

14.  A  piece  of  metal  weighs  14  Ibs.  in  ah*  and  12  Ibs.  in  water,     (a) 
What  is  its  specific  gravity?   (b)  its  density? 

15.  A  small  metal  ball  weighs  20  grams  in  air,  18  grams  in  water,  and 
17  grams  in  a  given  liquid.     Find  the  density  of  the  given  liquid. 

16.  The  density  of  lead  is  11.3  g.  per  cc.    What  is  the  weight  of  a  cu.  ft. 
of  lead? 

17.  A  specific  gravity  bottle  weighs  25  grams.     When  filled  with  water 
it  weighs  65  grams.     When  filled  with  a  given  salt  solution  it  weighs  75 
grams.     Find  the  density  of  the  salt  solution. 

18.  When  the  barometric  column  stands  at  a  height  of  74  cm.,  what 
is  the  pressure  of  the  atmosphere  in  (a)  grams  per  sq.  cm.?    (b)  dynes  per 
sq.  cm.?    (c)  pounds  per  sq.  in.? 

19.  A  given  mass  of  air  under  a  pressure  of  400  grams  per  sq.  cm.  has  a 
volume  of  100  cc.     If  the  pressure  be  increased  to  600  grams  per  sq.  cm., 
what  will  be  the  volume,  the  temperature  remaining  constant? 

20.  How  will  the  density  of  the  ah*  (problem  19)  be  affected  by  the 
increased  pressure,  and  how  much? 

21.  (a)  Under  a  pressure  of  one  atmosphere,  over  what  height  may 
water  be  siphoned?     (b)  When  the  barometric  pressure  is  70  cm.,  over 
what  height  may  water  be  siphoned? 

22.  A  sphere  having  a  volume  of   100  cc.  weighs  1  kilogram  in  air. 
What  is  its  weight  in  a  vacuum? 

23.  A  block  containing  2  cu.  ft.  weighs  100  Ibs.  in  air.     What  is  its 
weight,  referred  to  a  vacuum? 

24.  A  balloon  has  a  volume  of  60,000  cu.  ft.     It  is  filled  with  illumi- 
nating gas.     Find  (a)  the  weight  of  the  illuminating  gas  in  the  balloon; 
(b)  the  buoyant  force  on  the  balloon  due  to  the  weight  of  the  air  displaced. 

For  additional  Exercises  and  Problems,  see  Supplement. 


CHAPTER  V 
MOLECULAR    MECHANICS 

SOME  SPECIAL  PROPERTIES  OF  MATTER 

155.  Properties  of  Matter  Due  to  Molecular  Forces.     The 
properties  of  a  substance  are  those  characteristics  which  enable 
us  to  distinguish  it  from  other  substances.      Brittleness,  for 
example,  is  a  property  of  glass;   hardness  is  a  property  of  the 
diamond;  tenacity  is  a  property  of  iron,  etc.     There  are  a  great 
many  such  properties,  among  the  most  important  of  which  are 
those  due  to  molecular  forces.     The   relation  of   the   proper- 
ties of  a  substance  to  the  forces  operating  between  its  mole- 
cules is  very  well  illustrated  in  the  case  of  glass.     Experiment. 
If  a  glass  rod  be  bent  even  a  very  little  it  will  break.     We  say 
it  is  brittle.     If,  however,  the  rod  be  heated  in  a  flame  for  a 
few  minutes  it  will  bend  very  readily.     It  has  lost  its  property 
of  brittleness  and  now  has  the  property  of  flexibility. 

In  the  following  topics  we  shall  consider  a  number  of  proper- 
ties of  matter  which  are  due  mainly  to  the  action  of  molecular 
forces. 

156.  Cohesion  and  Adhesion.     The  attraction  which  exists 
between  molecules  of  the  same  kind  is  called  cohesion.     The 
attraction  between  molecules  of  unlike  kind  is  called  adhesion. 
The  particles  of  a  piece  of  chalk  are  held  together  by  cohesion. 
On  the  other  hand,  when  crayon  is  drawn  across  the  blackboard, 
a  chalk  mark  is  made;   the  attraction  between  the  chalk  and 
the  board  is  due  to  adhesion. 

Experiment.  If  a  piece  of  chalk  be  broken,  the  parts  can- 
not be  united  again  by  pressing  them  together  because  the 
molecules  cannot  be  brought  into  close  enough  contact  for  the 


MOLECULAR   MECHANICS 


107 


molecular  forces  to  operate.  If  two  pieces  of  lead,  how- 
ever, are  forced  together  by  a  twisting  motion,  the  parts  will 
cohere. 

157.  Examples   of   Molecular   Attraction.     A   broken   plate 
can  be  mended  by  means  of  cement,  a  kind  of  porcelain  in  a 
liquid  condition,  which  permits  of  the  molecules  being  brought 
into  intimate  contact.     The  blacksmith  unites  two  pieces  of 
iron  by  first  heating  them  red  hot  and  then  welding  (hammer- 
ing) them  together.     The  hammering  is  done  for  two  purposes, 
(a)  to  force  the  molecules  into  intimate  contact,  and  (b)  to  give 
the  iron  the  desired  shape. 

Experiment.  If  a  clean  glass  rod  be  thrust  into  water  and 
then  withdrawn  it  will  be  found  that  a  drop  of  water  clings 
to  the  glass.  In  like  manner  a  glass  plate 
clings  to  water,  Fig.  132.  This  means  that 
the  attraction  of  water  for  glass  (adhesion) 
is  greater  than  the  attraction  of  water  for 
water  (cohesion).  In  this  instance  adhe- 
sion is  greater  than  cohesion. .  On  pour- 
ing water  from  a  glass  or  pitcher,  the 
tendency  of  the  liquid  to  adhere  to  the 
vessel  is  well  illustrated  in  Fig.  133. 

158.  Tenacity.     Tenacity  is  that  prop- 
erty by  virtue  of  which  a  substance  resists  being  pulled  apart. 
A  strip  of  paper  is  quite  easily  pulled  apart;   its  tenacity  is 

relatively  small.     Iron  is  not  easily 
torn;  its  tenacity  is  great. 

Experiment.  If  an  iron  wire  and  a 
copper  wire  of  the  same  size  be  sus- 
pended from  a  support  and  weights 
added  to  the  free  ends  until  each 
wire  breaks,  it  will  be  found  that  a  much  greater  weight  is 
required  to  break  the  iron  than  the  copper.  The  relative 
breaking  or  tensile  strength  of  various  metals  is  about  as  fol- 
lows: Lead  1;  silver  14;  copper  20;  iron  30.  That  is,  an  iron 


FIG.  132 


FIG.  133 


108 


HIGH   SCHOOL  PHYSICS 


FIG.  134 


rod,  for  instance,  will  support  1.5  times  as  much  weight  as 
will  a  copper  rod  of  the  same  size. 

The  tensile  strength  of  steel  is  about  100,000  pounds  per 
square  inch.  This  means  that  a  steel  rod  of  good  quality, 
having  a  cross  sectional  area  of  one  square  inch,  will  support 
about  100,000  pounds.  Some  specially  drawn  steels,  however, 
such  as  are  used  in  the  manufacture  of  piano  wires,  may  have 
a  tensile  strength  as  great  as  300,000  pounds  per  square  inch. 
A  study  of  the  tensile  strength  of  building  materials  is  of  great 
importance  in  modern  engineering  practice. 

159.  Elasticity.  Elasticity  is  that  property  by  virtue  of  which 
a  body  tends  to  recover  its  shape  or  volume  after  being  distorted. 

A  body  is  distorted  when  it  is 
bent,  stretched,  twisted,  or  com- 
pressed. If  a  stick  be  bent,  Fig. 
134,  the  molecules  on  one  side 
may  be  conceived  of  as  being 
crowded  together,  and  on  the  other  side  pulled  apart.  The 
molecular  forces  on  the  one  side  are  repellant,  on  the  other 
attractive.  The  action  of  these  forces, 
tending  to  straighten  the  stick,  gives 
rise  to  the  property  of  elasticity.  If 
a  rubber  ball  be  dropped  upon  the 
floor  it  will  rebound,  due  to  its  elas- 
ticity. When  the  ball  strikes  the  floor 
it  flattens  somewhat,  the  molecules  in 
the  ball  next  to  the  floor  being  crowded 
together.  The  molecular  forces  within 
the  ball  cause  it  to  recover  its  shape, 
and  in  this  recovery  occurs  the  re- 
bound. If  a  steel  ball  be  dropped 
upon  a  marble  slab,  or  other  hard 
substance,  upon  which  there  is  a  coat- 
ing of  fine  dust,  Fig.  135,  it  will  flatten  somewhat  before 
rebounding,  as  shown  by  the  imprint  in  the  dust,  in  exactly 


FIG.  135 


MOLECULAR  MECHANICS  109 

the  same  manner  as  did  the  rubber  ball,  only  to  a  much  less 
degree. 

160.  Elasticity  and  Distortion.     Experiment.     Let  a  rod  be 
clamped  at  one  end  and  a  force  applied  to  the  other  so  that  the 
rod  is  bent  (distorted)  through  a  given  distance.     Now  let  the 
bending  force  be  removed,  and  if  the  rod  move  back  exactly 
to  its  original  position,  we  say  that  it  was  bent  within  its  elas- 
tic limits.     If,  however,  the  rod  be  bent  so  far  that  it  does  not 
go  back  to  its  former  position,  we  say  that  it  was  bent  beyond 
its  elastic  limit.     When  a  body  recovers  completely  its  original 
form  or  volume  after  being  distorted,  it  is  perfectly  elastic 
within  the  limits  of  its  distortion.     Liquids  and  gases  are  per- 
fectly elastic.     That  is,  no  matter  how  great  a  force  is  applied 
to  an  enclosed  volume  of  water  or  air,  for  instance,  or  how  long 
applied,  these  fluids  will  exactly  regain  their  -former  volume 
when  the  force  is  removed.     Solids,  on  the  other  hand,  are  per- 
fectly elastic  within  narrow  limits;    rubber,  within  wide  limits. 

161.  Hooke's  Law.    The  relation  between  the  force  applied 
to  an  elastic  body  and  the  resulting  distortion  of  the  body  is 
expressed  by   Hooke's  law,  which  states  that  within  the  elastic 
limits  of  a  body  the  distortion  is  proportional  to  the  force  applied. 

Experiment.     Hooke's  law  may  be  illustrated  by  the  appa- 
ratus of  Fig.  136.     A  rod  is  clamped  at  one  end,  the  other  being 


FIG.  136 

free  to  bend.  The  zero  position  of  the  free  end  is  noted,  and 
then  a  given  weight  is  added.  Suppose  that  this  cause  a  bend- 
ing of  1  inch.  Now  if  twice  as  much  weight  be  added,  the  rod 
will  bend  2  inches,  and  so  on  until  the  elastic  limit  is  reached. 
According  to  Hooke's  law  then,  if  a  given  force  will  bend,  twist, 


110 


HIGH  SCHOOL  PHYSICS 


or  stretch  a  body  through  unit  distortion,  the  application  of 
twice  as  much  force  will  produce  twice  the  bending,  twisting, 
or  stretching;  three  times  the  force,  three  times  the  distortion, 
and  so  on  until  the  limit  of  elasticity  of  the  body  is  reached. 

EXERCISES.  1.  If  a  force  of  10  Ibs.  stretch  a  given  wire  Tf7  in.,  what 
will  be  the  stretch  due  to  a  force  of  50  Ibs.? 

2.  Assuming  that  Hooke's  law  holds,  what  force  will  be  required  to 
stretch  the  wire  yV  in«? 

162.  The  Relation  of  the  Stretch  of  a  Metal  Rod  to  the  Force 
Applied.  Experiment.  Let  two  wires  of  the  same  length  and 
cross  section,  one  of  steel  and  the  other  of  copper, 
be  suspended  side  by  side,  Fig.  137,  and  weights 
added  until  each  wire  is  stretched  through  a  given 
distance,  0.01  inch  say.  It  will  be  found  that  it 
requires  nearly  twice  as  much  force  to  stretch  the 
steel  as  to  stretch  the  copper.  We  say,  therefore, 
that  the  elastic  constant,  or  coefficient  of  elasticity 
of  steel  is  about  twice  that  of  copper.  This  elastic 
constant,  or  coefficient  of  elasticity,  has  been  deter- 
mined for  all  ordinary  metals,  and  is  of  great  im- 
portance to  the  builder  and  the  engineer,  as  it  enables 
them  to  calculate  beforehand  the  length  that  a  given 
metal  will  stretch  when  subjected  to  a  given  force. 
163.  Some  Physical  Properties  of  Iron.  Since 
iron  in  some  form  enters  into  nearly  every  impor- 
tant building  operation,  its  physical  and  chemical 
properties  have  been  very  carefully  studied.  This 
is  particularly  true  with  reference  to  its  resistance  to 
forces  tending  to  stretch,  bend,  or  twist  it.  There 
are  a  number  of  different  kinds  of  iron,  the  most 
common  being  cast  iron,  wrought  iron,  and  steel. 
The  physical  properties  of  iron,  such  as  tenacity, 
brittleness,  elasticity,  etc.,  are  due  mainly  to  the  presence  of 
other  substances  such  as  carbon,  sulphur,  and  phosphorus. 
Cast  iron  is  a  brittle,  highly  crystalline  form,  and  its  physical 


FIG.  137 


MOLECULAR  MECHANICS  111 

properties  are  due  probably  to  the  relatively  high  percentage  of 
carbon  which  it  contains  —  2  to  3  per  cent.  It  expands  on 
solidifying,  and  to  this  property  is  due  its  use  in  molding.  The 
hot  metal  in  a  liquid  condition  is  poured  into  molds,  and  on 
solidifying  it  crystallizes  and  expands,  filling  exactly  the  outline 
of  the  mold,  after  which  it  contracts  somewhat.  Many  familiar 
articles  of  household  use  are  made  of  cast  iron,  such  as  kitchen 
stoves,  pots,  kettles,  etc. 

Wrought  iron  is  produced  by  burning  most  of  the  carbon  out 
of  cast  iron  by  exposing  the  molten  metal  to  a  stream  of  air 
and  by  working  the  iron  while  hot.  Wrought  iron  is  softer  and 
very  much  tougher  than  cast  iron  and,  unlike  the  latter,  can 
be  welded.  The  iron  used  by  the  blacksmith  in  most  of  his 
work  is  wrought  iron.  One  of  the  most  familiar  examples  of 
wrought  iron  is  the  common  nail. 

Steel  contains  less  carbon  than  cast  iron  and  more  than 
wrought  iron.  It  is  highly  elastic,  very  tenacious,  and  is  ca- 
pable of  being  tempered;  that  is,  hardened.  Nearly  all  edge 
tools  are  made  of  steel.  The  rails  of  car  tracks  are  in  general 
made  of  this  material,  as  are  also  many  of  the  beams  and  girders 
of  our  modern  iron  buildings. 

164.  Stiffness  and  Strength  of  Beams.  In  the  use  of  rods 
and  beams  in  building  operations  it  is  often  desirable  to  secure 
the  greatest  strength  and  stiffness  with  the  least  weight  of 
material.  To  accomplish  this,  beams  are  not  made  of  compact 
form,  but  rather  of  a  cross  section,  like  some  of  the  patterns 
shown  in  Fig.  138,  since  a  given  amount  of 
material  is  more  effective  in  resisting  a  bend 
or  a  twist  when  placed  some  distance  from 
its  center  of  cross  section.  For  this  reason 
the  steel  "  I  "  beam  is  commonly  used  in  the 
construction  of  buildings.  When  it  is  necessary  to  combine 
lightness  with  great  stiffness,  the  tubular  form  is  almost  always 
used,  as  in  the  frame  of  the  flying  machine,  the  bicycle,  etc. 
In  nature  we  find  many  examples  of  this  combination  of 


112  HIGH  SCHOOL  PHYSICS 

strength  and  lightness,  as  in  the  case  of  the  hollow  stalks  of 
grain,  the  bones  of  the  body,  and  the  quills  of  birds. 

It  must  not  be  understood,  however,  that  a  hollow  beam  is 
stronger  than  a  solid  one  of  the  same  dimensions.  A  hollow 
beam  is  stronger  than  a  solid  one  of  the  same  weight,  but  not  of  the 
same  dimensions.  If  the  saving  of  weight  and  material  were 
no  object,  beams  would  always  be  made  solid. 

165.  Ductility.  Ductility  is  that  property  by  virtue  of  which 
a  substance  may  be  drawn  out  into  threads.  Glass  at  ordinary 
temperatures  is  very  brittle,  but  when  heated  it  becomes  very 
ductile.  Experiment.  If  a  small  glass  tube  be  placed  in  a 
flame  for  a  few  moments  it  becomes  soft  and  pliable.  It  can 
then  be  drawn  out  into  very  fine  threads  which  are  flexible  and 
highly  elastic,  Fig.  139.  "  Glass  wool  "  which  is  sometimes 


FIG.  139 

used  for  laboratory  purposes  is  made  by  forcing  a  stream  of 
air  through  molten  glass,  which  by  this  means  is  blown  out  into 
exceedingly  fine  fibers,  somewhat  resembling  wool  in  color  and 
elastic  properties. 

Most  metals  are  ductile,  hence  are  capable  of  being  drawn 
out  into  wire.  Iron  and  copper  wire  are  good  examples  of  the 
ductile  properties  of  these  metals.  Platinum  is  one  of  the  most 
ductile  metals  known.  It  can  be  drawn  into  wire  so  fine  as  to 
be  almost  invisible. 

When  metals  are  drawn  into  wire  their  tenacity  is  in  general 
increased.  If  a  rod  of  iron,  for  example,  be  drawn  into  wire 
and  the  wire  be  twisted  into  a  rope  or  cable,  it  has  been  found 
that  the  cable  thus  formed  will  support  a  greater  weight  than 


MOLECULAR  MECHANICS 


113 


would  the  original  rod.  The  cable  also  has  the  advantage  of 
flexibility.  For  these  reasons  iron  cables  instead  of  iron  rods 
are  used  in  the  construction  of  certain  types  of  bridges. 

166.  Malleability.     Malleability  is  that  property  of  matter 
by  virtue  of  which  a  substance  may  be  beaten  out  into  thin 
sheets.     A  good  example  of  a  malleable  substance  is  the  tin 
foil  which  is  wrapped  around  many  articles  displayed  for  sale 
in  stores.     This  foil  is  made  by  hammering  or  rolling  the  metal 
tin  out  into  very  thin  sheets.     A  distinction  here  must  be  made 
between  the  metal  tin  and  the  so-called  "  tin  "  of  tinware. 
The  material  of  which  a  tin  cup,  for  example,  is  made  is  really 
sheet  iron  coated  with  a  very  thin  covering  of  tin. 

Gold  is  one  of  the  most  malleable  of  metals.  Sheets  of  gold 
may  be  beaten  out  so  thin  that  they  are  almost  transparent. 
It  is  estimated  that  300,000  such  sheets  laid  one  upon  the  other 
would  be  required  to  make  a  layer  an  inch  in  thickness. 

167.  Crystallization.     When  the  particles  of  a  substance  are 
arranged  in  a  definite   order,  the   substance   is   said  to  be  in 
a  crystalline  condition.      When  the  particles  have  no  definite 
arrangement,  the  substance  is  said  to  be  amorphous.     Ice  is 
a  good  example  of  a  crystalline  substance.     The  formation  of 
frost  on  the  window  pane  in  winter  gives  some  idea  of  the  great 
variety  of  crystalline  forms  which  water  assumes  on  freezing. 


FIG.  140.  —  Snowflake  Crystals 

Fig.  140  illustrates  a  few  of  the  almost  infinite  variety  of  the 
crystalline  forms  which  snowflakes  assume. 

Blackboard  crayon  is  an  example  of  an  amorphous  substance. 
Most  forms  of  glass,  such  as  window  glass,  tubing,  test  tubes, 
beakers,  etc.,  are  amorphous. 


114 


HIGH   SCHOOL  PHYSICS 


FIG.  141 


Carbon  occurs  in  nature  in  three  forms,  two  of  which  are 
crystalline  —  diamond  and  graphite;  and  the  third  amorphous 
—  coal,  charcoal,  lampblack. 

A  great  many  crystalline  substances  assume  definite  geo- 
metrical forms,  as  is  illustrated  by  Iceland  spar,  a  crystal  of 
which  is  shown  in  Fig.  141.     The  nature 
of  a  substance  is  often  determined  by  the 
crystalline  form  which  it  assumes. 

168.  Change  of  Volume  Due  to  Crystal- 
lization. Some  substances  on  crystallizing 
expand.  Water,  for  example,  in  freezing 
exerts  an  enormous  expansive  force,  as  is 
seen  in  the  bursting  of  water  pipes  in  win- 
ter, the  upheaval  of  cement  walks,  and  the 
disintegration  of  rocks.  Indeed  the  major 
portion  of  the  soil  is  formed  by  the  crum- 
bling of  the  rocky  material  of  the  earth's  crust,  due,  in  a  large 
part,  to  the  expansive  power  of  freezing  water. 

SURFACE  TENSION  AND  CAPILLARY  ACTION 

169.  The  Surface  of  a  Liquid.  One  of  the  most  striking  illus- 
trations of  the  action  of  molecular  forces  is  found  in  the  study 

of  the  surface  of  a  liquid.     Consider  the     & 

molecules  of  a  liquid,  as  shown  in  Fig. 
142.  Molecule  a,  for  example,  is  attracted 
equally  in  all  directions,  within  the  range 
of  the  molecular  forces,  hence  is  in  equi- 
librium. A  molecule  in  the  surface  layer 
6,  for  instance,  is  not  attracted  equally 
in  all  directions,  the  force  downward  being  greater  than  the 
force  upward,  because  the  molecules  of  water  attract  water 
with  a  greater  force  than  do  molecules  of  air.  Hence  it  fol- 
lows that  the  molecules  of  the  surface  layer  are  drawn  down- 
ward, and  are  therefore  a  little  closer  to  their  neighbors  than 
are  the  molecules  of  any  other  part  of  the  liquid.  This 


FIG.  142 


MOLECULAR   MECHANICS  115 

gives  rise  to  a  tension  in  and  parallel  to  the  surface  of  the 
liquid,  called  surface  tension.  The  surface  of  every  liquid  is 
under  a  state  of  tension  and  acts  exactly  as  if  it  were  a  stretched 
membrane. 

170.  Illustrations  of  Surface  Tension.  Experiment  1.  If  a 
wire  ring,  having  a  loop  of  thread  tied  to  it,  be  dipped  into  a 
soap  solution  and  then  with- 
drawn so  that  a  film  is  formed 
across  it,  the  loop  of  thread 
will  lie  on  the  face  of  the  film. 
If  now  the  film  be  punctured 
inside  the  loop,  the  thread 
will  spring  out  into  a  circle, 
the  tension  of  the  film  pulling 
the  loop  outward  equally  in  F 

all  directions,  Fig.  143. 

Experiment  2.     If  a  film  be  formed  across  the  mouth  of  a 
funnel  by  dipping  it  into  a  soap  solution,  it  will  be  observed 

that  the  film  creeps  down  the 
funnel  toward  the  small  end, 
due  to  its  tendency  (surface 
tension)  to  contract.  The  same 
phenomenon  may  be  seen  in 
the  case  of  the  contraction  of 
F  a  soap  bubble  blown  from  a 

pipe,  Fig.  144. 

Experiment  3.     Let  a  film  of  water  be  spread  out  over  a  clean 
glass  plate.     Now  put  a  drop  of  alcohol  on  the  water  and  the 
film  will  be  torn  asunder  at  the  point  of  contact, 
due  to  the  fact  that  the  surface  tension  of  water    ==^^^~^ 
is  greater  than  that  of  alcohol.  JTIG  ^45 

Experiment  4.    If  by  means  of  a  wire  holder  a 
needle  be  carefully  placed  upon  water,  the  membrane-like  sur- 
face will  cause  it  to  float,  Fig.  145. 

Certain  insects  may  be  seen  in  the  summer  time  running 


116  HIGH  SCHOOL  PHYSICS 

about  on  the  surface  of  still  water.     They  are  supported  by 
the  tough  surface  layer  of  the  liquid. 

171.  The  Spherical  Form  of  a  Drop  of  Liquid.     When  a  drop 
of  liquid  is  free  to  follow  its  tendencies,  unaffected  by  forces 
without,  surface  tension  draws  it  into  the  form  having  the 
least  surface;  that  is,  a  sphere.     Rain  drops  tend  to  become 
spherical  because  of  surface  tension;   the  drop  of  dew  on  the 
petal  of  the  rose  is  spherical  because  of  this  same  force.     Drops 
of  molten  lead  falling  from  a  great  height,  as  in  a  shot  tower, 
take  on  a  spherical  form  as  they  fall,  due  to  surface  tension, 
and,  cooling  as  they  descend,  retain  their  shape  when  they 
plunge  into  water  at  the  bottom  of  the  tower.     Small  globules 
of  mercury  are  very  nearly  spherical,  despite  the  great  weight 
of  the  metal,  because  of   the  tendency  of    the  surface  layer 
(surface  tension)  to  force  the  liquid  into  the  smallest  possible 
volume. 

172.  Oil  on  Water.     If  a  drop  of  light  oil  be  placed  on  water 
it  quickly  spreads  out  over  the  surface.     This  is  due  to  the  fact 
that  the  surface  tension  of  the  water  is  greater  than  that  of  the 
oil,  and  hence  the  latter  is  drawn  out  into  a  thin  film.     Now 
while  the  surface  tension  of  the  film  of  oil  is  less  than  that  of 
water,  it  possesses  another  property,  called  viscosity,  which 
gives  it  toughness.     Surface  viscosity  is  that  property  of  a  film 
by  virtue  of  which  it  may  be  stretched.     A  soap  bubble,  for 
example,  may  be  greatly  stretched  because  of  its  high  surface 
viscosity.     We  cannot  blow  water  bubbles  as  we  blow  soap 
bubbles  because  the  surface  viscosity  of  water  is  small.     For 
this  reason  the  wind  blowing  over  the  surface  of  water  easily 
breaks  it  up  into  ripples  and  waves.     A  film  of  oil  on  the  sur- 
face of  water,  on  the  other  hand,  is  not  easily  broken  because  of 
its  high  surface  viscosity;  hence  the  use  of  oil  in  stilling  a  rough 
sea  around  a  ship.     The  action  of  oil,  therefore,  in  "stilling 
troubled  waters  "  is  not  altogether  a  poetic  fancy. 

173.  Capillary  Action.     A  capillary  tube  is  one  having  a  very 
fine,  hair-like  bore.     If  one  end  of  a  capillary  tube  of  glass  be 


MOLECULAR   MECHANICS  117 


1 


thrust  into  water,  the  liquid  rises,  Fig.  146;   when  thrust  into 
mercury,  the  liquid  falls,  Fig.  147.    The  elevation  or  depression 
of  the  liquid  depends  on  the  nature  of  the 
curved  surface  within  the  tube.     When 
the  surface   is   curved   upward,  that  is, 
depressed  in  the  middle  as  in  water,  the 
liquid  rises;  when  curved  downward,  as 
in  mercury,  it  falls.     The  surface  of  all      pIG  ^45      pIG  14y 
liquids  forms  a  more  or  less  acute  angle 

with  solids;  hence  there  is  in  general  always  some  capillary 
action.  The  surface  of  water  forms  a  very  sharp  angle  with 
glass;  alcohol  very  nearly  a  right  angle  with  silver.  The  capil- 
lary action  in  the  case  of  water  and  glass  is  therefore  very 
pronounced;  that  between  alcohol  and  silver  very  slight.  If 
one  end  of  a  lump  of  sugar  be  dipped  into  a  liquid,  coffee  for 
instance,  the  liquid  will  rise,  due  to  capillary  action,  until  the 
lump  is  saturated.  The  rise  of  oil  in  the  wick  of  a  lamp, 
the  flow  of  the  melted  wax  up  the  wick  of  a  burning  candle, 
the  passage  of  ink  into  a  blotter,  and  the  flow  of  ink  in  the 
slit  of  a  pen  are  all  familiar  illustrations  of  capillary  action. 

174.  Cause  of  Capillary  Action.  The  factors  which  give 
rise  to  capillary  action  are  as  follows :  (a)  Nature  of  the  curved 
surface  of  the  liquid  in  contact  with  the  tube;  (b)  surface  ten- 
sion, which  furnishes  the  force  to  pull  the  liquid  up  the  tube  or 
to  cause  it  to  descend;  (c)  cohesion  between  the  molecules  of 
the  liquid. 

Experiment.  The  action  of  a  force,  such  as  surface  tension, 
along  a  curved  line  may  be  illustrated  by  a  rope  hanging  between 
two  supports,  as  shown  in  Fig.  148.  A  force  acting  on  a  curved 
line  tends  to  cause  it  to  become  a  straight  line.  Hence  if  the 
hand  exert  a  pull  analogous  to  the  surface  tension  of  the  liquid, 
the  rope  will  take  the  position  shown  by  the  dotted  line.  Now 
imagine  the  curved  surface  of  a  liquid  to  act  in  a  somewhat 
similar  manner.  The  curved  surface  tends  to  become  a  plane 
surface,  due  to  the  force  of  surface  tension;  then  the  force  of 


118 


HIGH   SCHOOL   PHYSICS 


attraction  between  the  liquid  and  the  tube  gives  a  new  curved 
surface,  which  again  tends  to  become  plane,  and  so  on,  until  the 


FIG.  148 


pull  upward  or  downward  is  just  counterbalanced  by  the  oppos- 
ing force  due  to  the  weight  of  the  liquid. 

175.  Laws  of  Capillary  Action.     The  three  laws  of  capillary 
action  may  be  stated  as  follows: 

I.  When  a  liquid  wets  the  tube,  it  will  rise;  when  it  does  not  wet 
the  tube,  the  liquid  will  fall. 

II.  The  elevation  or  depression  varies  inversely  as  the  diameter 
of  the  tube. 

III.  The  elevation  or  depression  decreases  as  the  temperature 
increases. 

The  first  law  is  illustrated  by  the  rise  of  water  and  the  de- 
pression of  mercury  in  glass  tubes.  The  second  law  states  the 
relation  between  capillary  action  and  the 
diameter  of  the  tube.  This  relation  is  illus- 
trated in  Fig.  149.  From  the  third  law  we 
learn  that  the  temperature  affects  capil- 
lary action.  The  fact  that  a  rise  of  temper- 
ature decreases  capillary  action  is  because 
an  increase  of  temperature  tends  to  dimin- 
ish the  forces  of  adhesion,  cohesion,  and 
surface  tension. 

176.  Application.     An  application  of  the  principle  of  capil- 
lary action  is  found  in  the  cultivation  of  the  soil  during  dry 
weather.     When  the  soil  is  closely  packed,  the  spaces  between 
its  particles  are  very  small;  hence  capillary  action  goes  on 


FIG.  149 


MOLECULAR   MECHANICS  119 

rapidly  and  the  water  within  the  soil  rises  to  the  surface  and 
evaporates.  If,  however,  the  soil  be  kept  well  cultivated  and 
is  loose,  the  spaces  between  the  particles  are  large  and  capil- 
lary action  goes  on  slowly.  Hence  it  follows,  other  things 
being  equal,  that  soil  which  is  well  cultivated  will  retain  its 
moisture  much  longer  than  soil  which  is  not  cultivated.  This 
is  one  of  the  important  principles  made  use  of  in  the  so-called 
"  dry  farming  "  in  certain  regions  of  the  West. 

DIFFUSION  AND  ABSORPTION 

177.  Diffusion  of  Gases  and  Liquids.  One  of  the  best  evi- 
dences of  molecular  motion  is  that  furnished  by  the  diffusion 
of  two  fluids.  Experiment*  If  a  tube  containing  hydrogen 
(atomic  weight  1)  be  inverted  over  a  similar  tube  containing 
oxygen  (atomic  weight  16)  the  two  gases  will  mix,  notwithstand- 
ing the  fact  that  the  lower  gas  (oxygen)  is  16  times  as  heavy  as 
the  upper.  The  diffusion  of  one  gas  into  another  is  due  to  the 
motion  of  the  molecules  of  the  gases.  Hydrogen  and  oxygen 
form  an  explosive  mixture.  The  fact  that  diffusion  actually 
takes  place  in  the  case  of  hydrogen  and  oxygen  may  be  demon- 
strated by  applying  a  lighted  match  to  either  tube. 
A  slight  explosion  occurs,  thus  showing  that  the 
gases  have  mixed. 

Experiment.     It  can  be  shown,  also,  that  a  heavy 
liquid  will  diffuse  upward  into  a  lighter  one.     In  a 
test  tube  place  a  solution  of  litmus.     By  means  of 
a  thistle  tube,  Fig.  150,  pour  some   sulphuric  acid 
into  the  tube  below  the  litmus  solution.     The  sul- 
phuric acid  is  considerably  heavier  than  the  litmus 
solution,  and  the  line  of  demarcation  between  the    JTIG    159 
two  is  sharply  defined.     In  a  few  hours  this  line  of 
separation  will  have  moved  upward,  showing  that  the  heavy 
acid  is  diffusing  up  into  the  lighter  liquid  above  it. 

Carbon  dioxide  (CO2)  is  about  1.5  times  as  heavy  as  air,  yet 


120 


HIGH   SCHOOL   PHYSICS 


it  mixes  readily  with  the  air,  due  to  the  tendency  of  fluids  to 
diffuse. 

178.  Diffusion     of     Gases     through     Solids.     Experiment. 
Lower  a  glass  jar  filled  with  some  light  gas,  such  as  hydrogen 
or  illuminating  gas,  over  a  porous  cup,  to  the  lower  end  of  which 
is  sealed  a  bent  glass  tube  containing  colored  liquid,  Fig.  151. 

The  light  gas  in  the  jar  diffuses  readily  through 
the  walls  of  the  porous  cup,  thus  giving  rise  to 
a  pressure  which  is  manifested  by  the  rise  of  the 
colored  liquid  in  the  bent  tube.  If  now  the  glass 
jar  be  removed  from  over  the  porous  cup,  the 
light  gas  which  has  diffused  into  the  cup  will  now 
diffuse  outward,  creating  thus  a  partial  vacuum 
within  the  cup.  This  is  shown  by  the  fact  that 
the  colored  liquid  in 'the  bent  tube  rises  toward 
the  cup,  above  its  position  of  equilibrium  ab. 

The  lighter  a  gas  the  more  readily  will  it  dif- 
fuse through  porous  solids.  The  rate  of  diffusion 
of  two  gases  through  a  porous  partition  is  in- 
versely proportional  to  the  square  root  of  their  densities.  For 
example,  the  weight  of  hydrogen  is  to  that  of  oxygen  as  the 
ratio  of  1: 16.  Hence  the  rate  of  diffusion  of  hydrogen  is  to 
the  rate  of  diffusion  of  oxygen  as  \/16:  VI  =  4-  !•  That  is, 
hydrogen  will  diffuse  4  times  as  fast  as  oxygen. 

Some  gases  will  diffuse  through  metals  under  certain  con- 
ditions.    Carbon  monoxide,  for  example,  will  dif- 
fuse readily  through  cast  iron  when  the  latter  is 
red-hot;    hydrogen,  also,  will  diffuse  through  red- 
hot  platinum. 

179.  Absorption.     Porous    solids   absorb    liquids 
and  gases.     The  absorption  of  a  liquid  by  a  solid 
may  be  illustrated  by  means  of  a  device  shown  in 
Fig.  152.     The  apparatus  consists  of  a  porous  cup 
into  the  end  of  which  is  fitted,  by  means  of  a  rubber 
stopper,  a  bent  glass  tube  containing  a  little  mercury.     If  the 


FIG.  152 


MOLECULAR   MECHANICS 


121 


cup  be  placed  in  a  beaker  of  water  the  mercury  will  rise  in  the 
outer  arm  of  the  tube,  thus  showing  an  increased  pressure  inside 
the  cup  due  to  the  absorption  of  water  by  its  walls. 

Some  solids  have  the  power  to  absorb  gases  to  a  remarkable 
degree.  This  is  especially  true  of  freshly  burned  charcoal,  as 
may  be  demonstrated  by  means  of  an  apparatus  as  shown  in 
Fig.  153.  Some  freshly  burned  charcoal,  cooled  to  room  tem- 
perature, is  put  into  a  wide-mouthed  bottle  filled  with  carbon 


\ 


CO 


CHARCOAL 


FIG.  153 


FIG.  154 


dioxide,  C02.  The  bottle  is  then  closed  with  a  rubber 
stopper  into  which  is  fitted  a  bent  glass  tube  as  shown.  The 
lower  end  of  the  tube  dips  into  a  beaker  of  colored  liquid. 
The  charcoal  quickly  absorbs  a  considerable  portion  of  the 
carbon  dioxide,  thus  creating  a  partial  vacuum  which  is  mani- 
fested by  a  rapid  rise  of  the  colored  liquid  in  the  tube. 

180.  Osmosis.  Experiment:  If  into  a  thistle  tube,  over 
the  end  of  which  there  has  been  fastened  a  membrane,  there 
be  put  a  solution  of  sugar  and  water  and  the  tube  immersed 
in  a  beaker  of  water,  Fig.  154,  it  will  be  observed  that  after  a 
time  the  liquid  in  the  tube  will  begin  to  rise.  The  water  in 


122  HIGH  SCHOOL  PHYSICS 

the  beaker  passes  through  the  membrane  more  readily  than 
the  sugar  solution  passes  out.  The  rise  of  the  liquid  in  the 
tube  is  due  to  a  force  called  osmotic  pressure.  The  process 
by  which  liquids  pass  through  membranes  is  called  osmosis.  A 
complete  and  satisfactory  explanation  of  the  causes  of  osmotic 
action  has  not  yet  been  found.  Suffice  it  to  say  that  osmosis 
is  due  to  molecular  forces  and  depends  upon  the  character  of 
the  liquids  separated  by  the  membrane,  and  also  upon  the 
nature  of  the  membrane  itself. 

The  principle  of  osmosis  plays  a  most  important  part  in  the 
life  of  plants  and  animals.  Soluble  food  ingredients  in  the  soil 
pass  through  the  thin  walls  of  the  rootlets  of  plants  by  osmosis. 
So,  too,  soluble  food  substances  in  the  human  body  enter  and 
leave  the  circulation  by  the  same  means.  Oxygen  of  the  air  also 
enters  the  blood  through  the  thin-walled  cells  of  the  lungs  by 
osmosis;  likewise  the  carbon  dioxide  of  the  blood  is  given  off. 

181.  Dialysis.  Substances  which  do  not  crystallize,  such  as 
starch,  gelatine,  etc.,  and  which  do  not  pass  through  mem- 
branes readily,  are  called  colloids;  substances  which  crystallize, 
as  sugars,  salts,  etc.,  and  which  pass  through  membranes  readily 
when  in  solution,  are  called  crystalloids.  The  separation  of  a 
crystalloid  from  a  colloid  is  called  dialysis.  If  arsenic,  for  ex- 
ample, is  mixed  with  ordinary  articles  of  food  it  may  be  sepa- 
rated from  the  starchy  constituents  of  the  solution  by  dialysis. 
The  mixture  is  put  into  a  vessel  having  a  membranous  bottom, 
and  the  whole  is  suspended  in  water.  The  arsenic  readily  passes 
through  the  membrane  into  the  water,  where  it  may  be  easily 
detected  by  chemical  analysis.  In  this  way  the  presence  of 
crystalloid  poisons  is  sometimes  detected  in  food. 


CHAPTER  VI 
HEAT 

TEMPERATURE 

182.  Nature  of  Heat.     Heat  was  formerly  believed  to  be  a 
subtle  fluid  called  caloric,  which  on  entering  a  body  produced 
the  phenomena  of  hotness,  burning,  etc.     About  the  end  of  the 
eighteenth  century,    however,    Count  Rumford  (Supplement, 
559)  performed  some  experiments  in  connection  with  the  bor- 
ing of  brass  cannon  which  demonstrated  that  the  caloric  theory 
(fluid  theory)  of  heat  is  untenable,  and  which  indicated  that 
there  is  some  close  relationship  between  heat  and  motion. 

In  1799  jSir  Humphrey  Davy  gave  the  deathblow  to  the 
caloric  theory  by  showing  that  two  pieces  of  ice  can  be  liquefied 
at  the  freezing  point  by  rubbing  them  together,  thus  proving 
that  heat  is  not  a  fluid,  but  a,  form  of  energy.  The  experiments 
of  Rumford  and  Davy  laid  the  foundation  for  the  modern 
kinetic  theory  of  heat^  which  assumes  that  heat  is  related  to 
molecular  motion.  According  to  this  theory,  if  the  molecular 
motion  of  a  body  be  increased  the  body  becomes  hotter;  if  the 
motion  be  decreased  it  becomes  cooler.  If  a  piece  of  metal  be 
struck  with  a  hammer,  both  the  hammer  and  the  metal  become 
heated,  because  of  the  increased  molecular  motion  due  to  the 
blow.  Also  if  a  piece  of  iron  be  thrust  into  the  fire  it  becomes 
heated,  because  of  the  increased  molecular  motion  imparted  by 
the  flame. 

Heat,  then,  may  be  defined  as  a  form  of  energy  due  to  the  molec- 
ular motion  of  a  body. 

183.  Sources  of  Heat.     The  principal  sources  of  heat  are:^ 
(a)  the  heavenly  bodies,  such  as  the  sun,  the  stars,  etc. ;  (b)  the 


124  HIGH  SCHOOL  PHYSICS 

interior  of  the  earth;  (c)  chemical  action,  as  in  the  combus- 
tion of  wood  or  coal;  (d)  electrical  energy,  as  in  the  heating  of 
the  filament  of  an  incandescent  lamp;  (e)  mechanical  sources, 
such  as  friction,  impact,  etc. 

184.  Temperature.     The  temperature  of  a  body  is  that  which 
determines  its  degree  of  hotness  or  coldness.     We  speak  of 
boiling  water  as  having  a  high  temperature;  of  ice  cold  water 
as  having  a  low  temperature.     The  temperature  of  a  body  is 
determined  by  the  average  kinetic  energy  of  its  molecules;  the 
greater  the  molecular  motion  the  higher  the  temperature. 

185.  Sensation  as  a  Measure  of  Temperature.     We  depend 
in  a  great  many  cases  upon  our  sensations  of  hot  and  cold  to 
determine  the  relative  temperature  of  bodies.     In  this  manner 
we  may  determine  that  a  steam  pipe  is  hot  and  that  ice  is  cold. 
This  primitive  method  of  determining  temperature,  however, 
is  not  reliable,  as  may  be  illustrated  by  a  simple  experiment. 
Take  three  basins  of  water,  one  hot,  one  cold,  and  one  tepid. 
Place  one  hand  in  the  hot  water  and  the  other  in  the  cold  and 
hold  them  there  for  a  moment.     Now  place  both  hands  in  the 
tepid  water.     The  hand  that  was  in  the  hot  water  will  feel 
cool  and  the  hand  that  was  in  the  cold  water  will  feel  warm. 
Thus  the  sensations  of  hot  and  cold  may  give  us  unreliable 
information  as  to  the  actual  temperature  of  the  water  in  the 
third  basin.     It  is  therefore  necessary  to  have  some  more  satis- 
factory means  of  measuring  temperature,  and  for  this  purpose 
we  use  a  thermometer. 

186.  Temperature    Measured    by   Expansion.     Experiment. 
Temperature  is  usually  measured  by  means  of  the  expansion  of 
some  substance  selected  as  a  suitable  medium.     The  expansion 
of  a  liquid  due  to  heat  may  be  illustrated  by  means  of  a  piece 
of  apparatus  as  shown  in  Fig.  155.  A  small  flask  having  a  glass 
tube  thrust  into  the  rubber  stopper  is  filled  with  colored  water. 
If  now  the  bulb  be  put  into  a  beaker  of  hot  water  two  things 
may  be  observed :    (a)  First  the  liquid  in  the  tube  falls  slightly 
and  then  (b)  it  rises  rapidly  to  a  given  height.     The  liquid  falls 


HEAT 


125 


at  first  because  of  tl^initiaj_e3qps^io^fjhe  ^glass  bu Ib;  the 
heat,  however,  soon  affects  the  liquid,  which,  expanding  more 
rapidly  than  the  glass,  rises  in  the  tube. 

In  choosing  a  thermometric  substance  it  is  im- 
portant to  select  a  liquid  which,  not  only  expands 
readily,  but  one  which  also  expands  at  a  uniform 
rate  with  respect  to  some  standard.  Mercury  is 
the  substance  which  is  usually  chosen  for  this 
purpose. 

187.  The  Mercury  Thermometer.  A  thermome- 
ter is  an  instrument  for  measuring  temperature. 
The  mercury  thermometer  consists  of  a  glass  tube 
containing  mercury  as  the  expanding  substance. 
The  thermometer  is  constructed  and  filled  as  fol- 
lows :  On  the  end  of  a  glass  tube  having 
a  capillary  bore  a,  Fig.  156,  there  is 
blown  a  thin- walled  bulb  b.  This  bulb 
and  a  short  portion  of  the  capillary  are 
filled  with  mercury  by  expelling  the  air 
from  the  bulb  by  heating,  and  then  thrusting  the 
open  end  of  the  tube  into  mercury,  which  rises  in 
the  tube  as  the  air  in  the  bulb  cools  and  contracts. 
The  instrument  is  now  heated  until  the  mercury 
expands  sufficiently  to  fill  the  entire  bore,  at  which 
time  the  tube  is  sealed  off  at  the  top,  as  shown 
in  c,  thus  leaving  it  air  tight.  When  the  ther- 
mometer cools  the  mercury  contracts  into  the 
lower  part,  leaving  the  major  portion  of  the 
capillary  free. 

188.  How  the  Fixed  Points  of  a  Thermometer 
are  Determined.  In  order  to  establish  a  ther- 
mometer scale  it  is  necessary  to  determine  two  fixed  points, 
the  freezing  point  and  the  boiling  point.  The  freezing  point 
is  determined  by  placing  the  bulb  and  part  of  the  stem  in 
finely  crushed  ice,  Fig.  157.  The  mercury  in  the  bulb  con- 


FIG.  155 


FIG.  156 


126 


HIGH   SCHOOL  PHYSICS 


100 


212 


tracts,  and  hence  the  thread  of  mercury  in  the  capillary  falls. 
The  point  at  which  it  comes  to  rest  is  marked.  This  is  called 
the  freezing  point  (F.P.) ;  it  is  the  temperature  at  which  water 

freezes  or  ice  melts,  the  two  points 
being  practically  the  same. 

The  boiling  point  is  determined 
by  suspending  the  thermometer  in 
steam  arising  from  water  boiling  un- 
der a  pressure  of  one  atmosphere. 
The  apparatus  used  in  determining 
the  boiling  point  is  shown 
in  Fig.  158.  The  required 
pressure  of  one  atmos- 
phere is  determined  by 
means  of  the  manometer 
gauge  m.  As  the  ther- 
mometer becomes  heated 
by  the  steam,  the  mercury 
rises  to  a  certain  point, 

where  it  remains  stationary.  ,A  mark  is  made  on 
the  scale  to  indicate  this  point,  which  is  called  the 
boiling  point  (B.P.). 

189.  The  Fahrenheit  Scale.     This  scale  was  first 
used  by  Fahrenheit,  a  German  scientist.     The  in- 
terval between  the  freezing  point  and  the  boiling 
point  is  divided  into  180  degrees,  usually  written 
180°.     The  zero  of  the  scale  is  set  at  32°  below  the 
freezing  point,  thus  making  the  interval  from  the 
zero  of  the  scale  to  the  boiling  point  212°.     There 
is  no  advantage,  as  we  now  know,  in  having  the  zero 
at  32°  below  the  freezing  point.      The  Fahrenheit 
scale  is  inconvenient   and  remains  in  use  largely 
through  custom. 

190.  The  Centigrade  Scale.     The  Centigrade  scale  was  first 
suggested  by  Celsius,   a  Swedish  astronomer  and  physicist. 


FIG.  157 


FIG.  158 


0 


-  LO  \     =LO 


FIG.  159 


HEAT  127 

The  interval  between  the  freezing  point  and  the  boiling  point 
is  divided,  as  the  word  centigrade  suggests,  into  one  hundred 
grades  or  degrees.  The  zero  of  this  scale  is  at  the  freezing 
point  of  water.  The  Centigrade  thermometer  is  used  in  all 
scientific  measurements  of  temperature  and  is,  on  account  of 
the  simplicity  and  convenience  of  its  scale,  coming  more  and 
more  into  common  use. 

191.  Comparison  of  Centigrade  and  Fahrenheit  Scales.  In 
Fig.  159  the  two  scales  are  drawn  side  by  side  for  comparison. 
Since  the  interval  between  the  freezing  point  and  the  boiling 
point  is  the  same  for  both  scales,  differing  only  in  the  number 
of  units  marked  on  each,  we  may  write 

100  units  of  the  C.  scale  =180  units  on  the  F.  scale, 
1  C.  unit  =  |  F.  unit, 
1  F.  unit  =  f  C.  unit 

Now,  bearing  in  mind  that  to  change  from  one  scale  to  the 
other  it  is  necessary  to  reckon  from  some  fixed  point  such  as 
the  freezing  point,  and  to  do  this  we  must  always  take  into 
account  the  32  units  between  zero  and  the  freezing  point  of 
the  Fahrenheit  scale,  the  above  equations  may  be  expressed  in 
the  following  convenient  forms: 

To  change  from  C.  to  F.:   (C.  X  f )  +  32  =  F. 
To  change  from  F.  to  C. :   (F.  -  32)  X  f  =  C. 

Examples,  (a)  A  reading  of  20°  on  the  C.  scale  is  equivalent  to 
what  reading  on  the  F.  scale?  Solution :  (20  X  f )  +  32  =  68°  F. 

(6)  A  reading  of  —20°  C.  is  equivalent  to  what  reading  on 
the  F.  scale?  Solution:  (-20  X  f)  +  32  =  -  4°  F. 

(c)  A  reading  of  +113°  F.  is  equivalent  to  what  reading  on 
the  C.  scale?     Solution:  (113  -  32)  X  f  =  45°  C. 

(d)  A  reading  of  +  23°  F.  is  equivalent  to  what  reading  on 
the  C.  scale?     Solution :  (23  -  32)  X  -*-  =  -  5°  C. 

(e)  A  reading  of  —13°  F.  is  equivalent  to  what  reading  on 
the  C.  scale?     Solution:  (-  13  -  32)  X  |  =  -  25°  C. 


128 


HIGH   SCHOOL  PHYSICS 


EXERCISES.  1.  Give  for  the  following  C.  readings  their  equivalents 
on  the  F.  scale:  (a)  +  10°  C.;  (b)  -  10°  C.;  (c)  +  30°  C.;  (d)  -  30°.  C.; 
(e)  -  40°  C. 

2.  Give  for  the  following  F.  readings  their  equivalents  on  the  C.  scale: 
(a)  +  32°  F.;  (b)  +  77°  F.;  (c)  +  5°  F.;  (d)  -  4°  F.;  (e)  -  40°  F. 

192.  Limitations  of  the  Mercury  Thermometer.  The  limi- 
tations of  a  thermometric  substance  are,  in  general,  fixed  by  its 
freezing  point  and  its  boiling  point.  Mercury  freezes  at  —  39° 
C.,  and  consequently  cannot  be  used  for  measuring  temperatures 
below  this  point.  For  measuring  temperatures  below  —  39°  C. 
alcohol  is  often  used  as  the  thermometric  substance.  (Sup- 
plement, 560.)  This  liquid  is  colored  red  or  blue  to  render 
it  visible  against  the  glass.  The  freezing  point  of  alcohol  is 
-  130°  C.;  its  boiling  point,  +  78°  C. 

Me'rcury  boils  at  357°  C.,  under  atmospheric  pressure,  but 
the  boiling  may  be  prevented  by  an  increase  of  pressure.  When 
it  is  desired  to  use  a  mercury  thermometer  for  the  measure- 
ment of  temperatures  higher  than  its  boiling  point,  it  is  neces- 
sary to  fill  the  space  above  the  mercury  in  the  tube  of  the 
thermometer  with  some  inert  gas,  usually  nitrogen.  Upon 
the  expansion  of  the  mercury  the  enclosed  nitro- 
gen is  compressed  and  the  mercury  is  pre- 
vented from  boiling.  It  is  thus  not  uncommon 
to  find  mercury-in-glass  thermometers  reading 
up  to  500°  C. 

193.  The  Air  Thermometer.  One  of  the 
earliest  and  simplest  instruments  for  measur- 
ing temperature  is  the  air  thermometer,  a  device 
such  as  is  shown  in  Fig.  160.  It  consists  of  a 
glass  bulb  and  a  stem  supported  vertically,  the 

_        open  end  of  the  tube  being  immersed  in  a  col- 

~"  T-/  ored  liquid.     A  small  quantity  of  the  air  in  the 

JP  IG.    1DU  t 

thermometer  is  driven  out  by  heating  the 
bulb,  thus  allowing  the  colored  liquid  to  rise  a  short  distance 
up  the  tube.  If  the  temperature  now  rise,  the  air  in  the  bulb 


HEAT  129 

expands  and  the  colored  liquid  in  the  stem  falls.  When  the 
temperature  falls,  the  liquid  in  the  stem  rises.  The  air  ther- 
mometer is  very  sensitive  and,  in  a  modified  form,  is  used  in 
making  certain  accurate  scientific  measurements. 

194.  The  Clinical  Thermometer.     This  instrument  is  used 
by  physicians  and  nurses  in  taking  the  temperature  of  the 
human  body.     It  is  a  mercury-in-glass  thermometer, 

Fig.  161,  and  is  characterized  by  having  a  narrow 
constriction  c  in  the  capillary.  When  the  thermom- 
eter cools  the  mercury  thread  breaks  at  this  point, 
leaving  the  column  in  the  tube  as  it  was  at  the 
highest  temperature  while  in  contact  with  the  body. 
Thus  the  reading  of  the  instrument  may  be  made 
sometime  after  the  temperature  is  taken.  Before  this 
thermometer  can  be  used  again,  the  mercury  in  the 
stem  must  be  forced  down  into  the  bulb  by  giving  the 
instrument  a  jerking  motion. 

MEASUREMENT  OF  HEAT 

195.  Distinction  between  Temperature   and    Quan- 
tity  of   Heat.     It  is  important  that  a  distinction  be 
made  between  the  temperature  of  a  body  and  the 
quantity  of  heat  which  it  contains.     For  example,  a 
tin  cup  of  boiling  water  has  a  temperature  very  much 
higher  than  that  of  the  water  in  a  lake  under  ordi- 
nary summer  conditions,  yet  the  quantity  of  heat  in 
the   water  of  the   lake  is  many  times  greater    than 

that  of  the  cup.     The   temperature   of  a   body   de-  FIG>  151 
pends  on  the  average  kinetic  energy  of  its  molecules; 
the  quantity  of  heat  in  the  body  depends  not  only  upon  its 
temperature,  but  also  upon  its  mass. 

6.  Unit  Quantity  of  Heat.  There  are  two  units  employed 
in  the  measurement  of  heat :  (a)  the  calorie,  based  on  the  gram 
mass  and  the  Centigrade  scale,  and  (b)  the  British  thermal  unit 


130  HIGH   SCHOOL   PHYSICS 

(B.T.U.),  based  on  the  pound  mass  and  the  Fahrenheit 
scale. 

\J A  calorie  is  the  quantity  of  heat  required  to  raise  the  tempera- 
ture of  one  gram  of  water  one  degree  Centigrade.  Thus  the  quan- 
tity of  heat  required  to  raise  one  liter  of  water  (1000  grams) 
from  20°  C.  to  the  boiling  point  (100°  C.)  is  1000  X  80  = 
80,000  calories. 

/A  British  thermal  unit  (B.T.U.)  is  the  quantity  of  heat 
required  to  raise  one  pound  of  water  one  degree  Fahrenheit.  For 
example,  the  number  of  B.T.U.  required  to  raise  one  gallon  of 
water  (8  pounds)  from  70°  F.  to  the  boiling  point  (212°  F.)  is 
8  X  142  =  1136  B.T.U. 

197.  Specific    Heat.     All    bodies    do    not    have    the    same 
capacity  for  heat.     If  we  take  one  pound  of  water  and  one  pound 
of  iron  and  raise  the  temperature  of  each  one  degree,  it  will  be 
found  that  while  the  water  will  require  one  unit  of  heat,  the 
iron  will  require  only  about  one-tenth  of  a  unit.     The  specific  \, 
heat  of  a  substance  is  the  number  of  units  of  heat  required  to 
raise  the  temperature  of  unit  mass  one  degree.     The  specific  heat 
of  water  is  1;  that  is,  it  requires  1  calorie  to  raise  1  gram  1°  C.; 
or  in  English  units,  it  requires  1  B.T.U.  to  raise  1  pound  1°  F. 
When  we  say  that  a  substance,  as  mercury  for  example,  has  a 
specific  heat  of  0.033,  we  mean  that  it  requires  0.033  of  a  unit 
(calories  or  B.T.U.)  to  raise  the  temperature  of  unit  mass 
(gram  or  pound)  one  degree  (Centigrade  or  Fahrenheit). 

198.  How  to  Find  the  Specific  Heat  of  a  Body.     Experiment. 
One  of  the  simplest  means  of  determining  the  specific  heat  of  a 
body  is  known  as  the  method  of  mixtures.     A  hot  body  is  brought 
in  contact  with  a  cooler  body;  the  hot  body  loses  heat  and  the 
cool  body  gains  heat.     Suppose  that  we  wish  to  find  the  specific 
heat  of  lead.     Put  200  grams  of  lead  shot  into  a  test  tube  and 
close  the  mouth  of  the  tube  loosely  with  a  plug  of  cotton. 
Suspend  the  tube  for  several  minutes  in  boiling  water  until  the 
lead   comes  to  the  temperature   of  the  water,  which   should 
be  determined  by  means  of  a  thermometer.     Have  at  hand 


HEAT  131 

a  beaker  containing  a  known  mass  of  water,  200  grams  say. 
Determine  the  temperature  of  this  water,  and  then  quickly 
transfer  the  shot  from  the  test  tube  to  the  beaker.  Stir  gently 
with  a  thermometer  until  the  mixture  in  the  beaker  (shot  and 
water)  comes  to  a  constant  temperature,  which  should  be  noted. 
We  now  have  the  following  data :  The  mass  of  the  lead  and  its 
change  (fall)  in  temperature;  the  mass  of  the  water  and  its 
change  (rise)  in  temperature.  From  this  we  may  compute 
the  specific  heat  of  the  lead. 

The  calculation  of  the  specific  heat  of  a  body  by  the  method 
of  mixtures  is  based  on  the  assumption  that  the  heat  lost  by 
one  body  is  equal  to  the  heat  gained  by  the  other  body;  that  is, 
in  the  particular  case  under  consideration,  the  heat  lost  by  the 
lead  is  equal  to  the  heat  gained  by  the  water.  Now  the  heat 
lost  or  gained  by  the  body,  measured  in  calories  or  B.T.U.,  is 
equal  to  the  mass  of  the  body  times  the  change  in  temperature, 
times  the  specific  heat ;  therefore,  we  may  write 

heat  lost  by  lead  =  heat  gained  by  water ;  that  is, 
mass  lead  X  ch.  tern.  X  sp.  h.  =  mass  water  X  ch.  tern.  X  sp.  h. 
m  X  t  X  s  =  m'  X  t'  X  s' 

in  which  m  is  the  mass  of  the  body  losing  heat,  t  its  change  in 
temperature,  s  its  specific  heat;  and  m'  the  mass  of  the  body 
gaining  heat,  t'  its  change  in  temperature,  s'  its  specific  heat. 
This  last  equation  expresses  in  a  general  and  very  convenient 
manner  the  relation  of  the  heat  lost  to  that  gained,  and  enables 
us  to  determine  any  one  of  the  six  factors,  provided  five  are 
given. 

Example.  To  find  the  specific  heat  of  lead  from  the  following 
data:  Mass  of  lead,  200  grams;  temperature  of  the  lead  in  hot 
water,  98°  C.;  mass  of  water  in  the  beaker,  200  grams; 
temperature  of  water  before  lead  was  put  into  the  beaker, 
20°  C.;  final  temperature  of  water,  22.3°  C.  Solution:  Assum- 
ing that  the  heat  lost  by  the  lead  is  equal  to  the  heat  gained  by 
the  water,  we  may  write 


132  HIGH  SCHOOL  PHYSICS 

m  X  t  X  s  =  mf  X  t'  X  sf 

200  X  (98  -  22.3)  X  s  =  200  X  (22.3  -  20)  X  1 
s  =  0.03 

Example.  In  the  preceding  example  it  was  assumed  that  all 
the  heat  lost  by  the  lead  was  gained  by  the  water,  no  account 
being  taken  of  the  heat  absorbed  by  the  beaker.  In  making 
accurate  determinations  of  specific  heat,  however,  it  is  always 
necessary  to  calculate  the  amount  of  heat  absorbed  by  the  con- 
taining vessel,  as  illustrated  by  the  following:  Suppose  that 
an  iron  ball  of  mass  52  grams  having  a  temperature  of  100°  C. 
be  dropped  into  200  grams  of  water  at  20°  C.,  contained  in  a 
copper  calorimeter  having  a  mass  of  100  grams.  The  resulting 
temperature  of  the  calorimeter  and  its  contents  is  22.2°  C.  The 
specific  heat  of  copper  is  0.09.  Find  the  specific  heat  of  the 
iron.  Solution :  In  making  a  calculation  of  this  sort  we  assume 
that  the  heat  lost  by  the  iron  is  gained  by  the  water  and  the  calo- 
rimeter together;  therefore,  we  may  write 

m  X  t  X  s  =  mf  X  t'  X  s'  +  m"  X  t"  X  s" 

52  X  77.8  X  s  =  200  X  2.2  X  1  +  100  X  2.2  X  .09 

s  =  0.113 

EXERCISES.  3.  A  piece  of  nickel  'having  a  mass  of  114  grams  at  100°  C. 
is  dropped  into  100  grams  of  water  at  10°  C.  The  resulting  temperature 
of  the  water  is  20°  C.  Find  the  specific  heat  of  the  nickel,  neglecting 
the  heat  lost  to  the  containing  vessel. 

4.  One  kilogram  of  water  and  one  kilogram  of  iron,  each  at  a  tempera- 
ture of  100°  C.,  are  cooled  to  20°  C.  How  much  heat  in  calories  is  given 
out  by  each? 

6.  A  person  drinks  300  grams  of  ice  water  which  comes  to  the  tem- 
perature of  the  body  (98.5°F.).  How  many  calories  of  heat  are  taken  up 
by  the  water? 

For  Table  of  Specific  Heats,  see  Supplement,  605. 

EXPANSION 

199.  Expansion  of  Solids.  When  a  solid  is  heated  it,  in 
general,  expands;  when  cooled,  it  contracts.  There  are  a  few 


HEAT 


133 


exceptions  to  this  rule,  as  for  example,  stretched  india  rubber 
and  iodide  of  silver,  both  of  which,  within  a  certain  range, 
contract  when  heated. 

Experiment.  If  a  metal  rod  be  adjusted  as  shown  in  Fig.  162 
and  heat  applied*  by  means  of  a  Bunsen  burner,  the  rod  will 
lengthen,  causing  the  pointer  to  rotate,  as  the  free  end  of  the  rod 
rolls  over  the  needle.  The  increase  in  length  due  to  a  rise  in 
temperature  is  called  linear  expansion. 


-*7 


as 

\ 

\ 

>  A 

^ 

FIG.  162 


FIG.  163 


Experiment.  The  ring  and  ball  experiment,  Fig.  163,  illus- 
trates the  fact  that  solids  on  being  heated  increase  in 
volume.  When  both  the  ring  and  the  ball  are  of  the  same  tem- 
perature the  ball  passes  readily  through  the  ring.  When  the 
ball  is  heated  it  will  not  pass  through  the  ring.  The  increase  in 
volume  due  to  a  rise  in  temperature  is  called  cubical  expansion. 

200.  Coefficient  of  Expansion.  All  solids  do  not  expand 
equally  for  the  same  change  in  temperature.  For  example,  for 
a  given  change  of  temperature  a  brass  rod  will  expand  more 
than  will  a  similar  copper  rod ;  and  copper,  in  turn,  will  expand 
more  than  iron.  It  is  important,  then,  to  know  something 
of  the  rate  at  which  metals  expand  for  given  changes  of  tem- 
perature, the  ratio  expressing  such  expansion  being  called  the 
coefficient  of  expansion.  The  coefficient  of  linear  expansion  of 
a  substance  is  its  increase  in  length  per  degree  per  unit  of  length. 

This  may  be  written 

increase  in  length 
Coefficient  of  linear  expansion  =  — — — r~; — 7^ — 

original  length  X  ch.  tern. 


134 


HIGH   SCHOOL  PHYSICS 


Example.  A  metal  rod  1  meter  in  length  expands  2  milli- 
meters when  its  temperature  is  increased  from  0°  C.  to  120°  C. 
Find  its  coefficient  of  linear  expansion. 


Solution:  C.  of  L.E.  = 


0.2 
100"x~120 


1 

60,000 


EXERCISES.  6.  At  a  temperature  of  0°  C.  an  iron  pipe  is  100  ft.  long. 
Its  length  increases  to  100.12  ft.  when  heated  to  100°  C.  by  steam  passing 
through  it.  Find  the  coefficient  of  expansion  of  iron. 

7.  A  brass  rod  having  a  coefficient  of  linear  expansion  of  0.000018  has 
a  length  of  180  cm.  at  0°  C.     What  will  be  its  length  at  100°  C.? 

8.  A  steel  rail,  such  as  is  used  on  railroad  tracks,  30  ft.  long  and  having 
a  coefficient  of  linear  expansion  of  0.000012,  will  increase  in  length  how 
many  inches  when  the  temperature  changes  from  0°  C.  to  50°  C.? 

201.  The  Compound  Bar.  If  two  strips  of  different  metals, 
such  as  brass  and  iron,  be  riveted  together,  Fig.  164,  and  the 
compound  bar  thus  formed  be  heated,  it  will  bend  in  the  form 
shown  in  b,  due  to  the  fact  that  the  coefficient  of  expansion  of 
brass  is  greater  than  that  of  iron.  Some  of  the  applications 
of  the  compound  bar  principle  are  illustrated  in  the  following 

topics. 

Of 

B 


FIG.  165 


202.  The    Alarm     Thermometer.      In    Fig.    165    there    is 
shown  a  device  for  automatically  closing  an  electric  circuit  by 
the  bending  of  the  compound  bar  B.     If  the  bar  be  heated,  the 
brass  will  expand  more  rapidly  than  the  iron,  and  thus  cause 
the  bar  to  bend  toward  A  until  electric  contact  is  made.     Such 
a  device  is  sometimes  used  to  give  alarm  in  case  of  fire. 

203.  The  Compound  Balance  Wheel.     The  balance  wheel  of 
a  watch  serves  the  same  purpose  as  the  pendulum  in  a  clock. 


HEAT 


135 


FIG.  166 


If  the  temperature  increase,  the  length  of  the  spokes  change 

thereby,  and  also  the  elasticity  of  the  hairspring,  causing  a 

change  in  the  period  of  vibration.     To  offset  this  change  in  the 

rate  of  vibration  the  rim  of  the  wheel  is  made 

of  a  compound  bar,  the  metals  of  which  are 

arranged  in  such  a  way  that  the  outer  one 

expands  much  more  'rapidly  than  the  inner 

one,  thus  causing  the  ends  A  and  B,  Fig.  166, 

to  bend  inward.     In  this  manner  the  time  of 

vibration  of  the  wheel  may  be  kept  practically 

constant. 

204.  The  Compensation  Pendulum.  We  have  seen  that  a 
change  in  temperature  tends  to  produce  a  change  in  the  length 
of  a  body.  Now  any  variation  in  the  length  of  its  pendulum 
will  change  the  rate  of  a  pendulum  clock.  Several  devices,  Fig. 
p  167,  have  therefore  been  employed  to  keep 
the  length  constant,  one  such  being  the 
so-called  gridiron  pendulum,  in  which  the 
lengthening  of  the  rods  marked  s,  usually 
of  steel,  tends  to  lower  the  bob,  while  the 
expansion  of  the  rods  6,  usually  of  brass, 
raises  the  bob,  and  thus  the  expansion  of 
one  set  of  rods  is  made  to  counteract  the 
effect  of  the  other.  In  the  mercury  com- 
pensating pendulum  the  lengthening  or 
shortening  of  the  rod  is  counteracted  by 
a  rise  or  fall  of  the  center  of  gravity  due 
to  the  expansion  of  the  mercury  in  the  two 
glass  vessels  forming  the  bob. 

205.  Further  Applications  of  the  Prin- 
ciples of  Expansion.  The  fact  that  met- 
als expand  when  heated  and  contract  when 
cooled  has  to  be  taken  into  account  in  a  great  many  building 
and  engineering  operations.  For  example,  in  the  construction 
of  a  railway  track,. space  must  be  left  between  the  ends  of  the 


FIG.  167 


136 


HIGH   SCHOOL   PHYSICS 


rails  to  accommodate  the  expansion  due  to  a  change  of  temper- 
ature of  about  50°  C.  from  winter  to  summer. 

Expansion  joints  are  sometimes  fitted  into  steam  pipes  to 
give  some  freedom  of  motion  as  the  pipe  expands  and  contracts. 
Iron  bridges  are  sometimes  left  free  at  one  end  and  constructed 
so  as  to  move  upon  a  roller,  as  the  material  of  the  bridge  changes 
in  length  with  change  of  temperature,  Fig.  168. 


X1X1X1X 


FIG.  168 

206.   The  Force  of  Expansion  and   Contraction.     The  force 
exerted  by  metals  when  expanding  or  contracting  is  usually 

very  great.  It  is  estimated 
that  it  would  require  a  pres- 
sure of  nearly  10,000  pounds 
per  square  inch  to  keep  mer- 
cury from  expanding  when 
heated  from  0°  C.  to  10°  C. 
Tires  are  heated  and  then 
slipped  upon  wagon  wheels, 
Fig.  169.  In  cooling,  the 
tire  grips  the  wheel  with  a 
FIG.  169  great  force.  Boiler  plates 

are    also   fastened   together 

by  heated  rivets;  when  the  rivets  cool  they  contract,  forming 
rery  tight  joints. 

*  207.  Expansion  of  Liquids.  Liquids  in  general  expand  when 
heated  and  contract  when  cooled.  Since  liquids  conform  to  the 
shape  of  the  containing  vessel,  it  follows  that  in  determining 
their  coefficients  of  cubical  expansion,  account  must  be  taken  of 


HEAT  137 

the  expansion  of  the  vessel  as  well  as  that  of  the  liquid.  Like 
solids,  liquids  have  different  coefficients  of  expansion.  For 
example,  the  coefficient  of  expansion  of  alcohol  is  about  0.00104; 
that  of  mercury,  0.000182. 

208.  Anomalous  Expansion  of  Water.  Water  is  a  partial 
exception  to  the  rule  that  liquids  expand  when  heated  and 
contract  when  cooled.  If  a  quantity  of  water  at  0°  C.  be  heated, 
its  volume  decreases  until  the  temperature  reaches  4°C.,  after 
which  the  volume  increases  as  the  temperature  rises,  at  8°C. 
the  volume  being  about  the  same  as  at  0°C.  At  4°C.,  therefore, 
a  given  quantity  of  water  has  its  'least  volume,  and  hence  its  greatest 
density.  This  fact  is  of  great  importance  in  nature,  as  is  illus- 
trated by  the  freezing  of  water  in  a  lake  in  winter.  When  the 
temperature  falls,  the  water  at  the  surface  reaches  its  maxi- 
mum density  at  4°C.  and  sinks  to  the  bottom,  thus  forcing 
the  warmer  water  upward.  This  goes  on  until  the  entire  lake 
reaches  a  temperature  of  4°C.,  after  which  the  temperature  of 
the  water  at  the  surface  falls  to  0°  C.  and  begins  to  freeze. 
Since  the  density  of  ice  is  less  than  that  of  water  at  the  freezing 
point,  it  remains  at  the  surface.  The  temperature  of  the  water 
at  the  bottom  of  a  pond  or  a  lake  in  winter  is,  therefore,  4°C.; 
indeed,  the  temperature  of  the  deep  water  of  our  great  lakes 
remains  at  about  this  point  throughout  the  year. 
*  209.  Expansion  of  Gases.  With  respect  to  their  expansion, 
gases  differ  from  solids  and  liquids  in  two  very  important 
particulars,  (a)  For  a  given  change  of  temperature,  the  expan- 
sion of  gases  is  much  greater  than  that  of  solids  or  liquids 
under  ordinary  conditions;  (b)  all  gases  have  practically  the 
same  coefficient  of  expansion. 

The  coefficient  of  expansion  of  a  gas  is  TTS-  That  is,  if  the 
temperature  of  a  given  volume  of  gas  at  0°  C.,  and  under  con- 
stant pressure,  be  increased  1°  C.,  it  will  expand  ^-f^-  of  its  vol- 
ume; if  it  be  heated  10°  it  will  expand  ^Vs,  and  so  on,  the 
expansion  in  each  case  being  calculated  with  reference  to  the 
volume  at  0°  C.  If  the  gas  be  cooled,  the  pressure  remain- 


138  HIGH   SCHOOL   PHYSICS 

ing  constant,  it  will  contract  ^H  of  its  volume  at  0°  C.,  per 
degree. 

210.  Absolute   Temperature.     If  a  gas  enclosed  within  a 
vessel  of  constant  volume  be  heated,  the  pressure  which  it 
exerts  will  increase;    if  the  gas  be  cooled,  the  pressure  will 
decrease.     The  pressure  exerted  by  a  gas  at  0°  C.  is  changed 
•2T3  per  degree  of  change  of  temperature.     Thus  it  will  be  noted 
that  the  pressure  coefficient  is  the  same  as  that  of  the  volume 
coefficient,  namely,  ^-7-?.     Now,  suppose  that  the  temperature 
of  this  gas  could  be  reduced  273°  below  0°  C.,  it  is  evident  that 
its  pressure  would  become  zero;  which  would  mean  that  its 
molecular  motion  would  also  be  zero.     Since  heat  is  due  to 
molecular  motion,  it  follows  that  under  these  conditions  there 
would  be  no  heat.     This  temperature,  273°  below  0°  C.,  is  called 
the  absolute  zero,  and  a  scale  based  on  this  zero  is  called  the 
Absolute  scale. 

Readings  on  the  Centigrade  scale  may  be  changed  to  those  on 
the  Absolute  scale  by  simply  adding  273  to  the  C.  values. 

Example.  Change  the  following  Centigrade  readings  to 
Absolute:  (a)  0°C.;  (b)  +20°C.;  (c)  -  20°  C.  Solution: 
(a)  0°  C.  =  0  +  273  =  273°  Abs.;  (b)  +  20°  C.  =  20  +  273  = 
293°  Abs.;  (c)  -  20°  C.  =  -  20  +  273  =  253°  Abs. 

EXERCISES.  9.  Give  the  absolute  values  for  the  following  Centigrade 
readings:  (a)  +  10°  C.;  (b)  —  10°  C.;  (c)  boiling  point  on  C.  scale. 

10.  Give  the  equivalent  Centigrade  values  for  the  following  readings 
on  the  Absolute  scale:  (a)  243°  Abs.;  (b)  303°  Abs.;  (c)  0°  Abs. 

211.  Gay-Lussac's    Law.     The   law   of   Gay-Lussac,    often 
called  the  law  of  Charles  (Supplement,  561),  takes  its  name  from 
Gay-Lussac,  a  French  physicist,  who  was  one  of  the  first  to 
announce  the  law  governing  the  relation  between  the  volume 
and  the  temperature  of  a  gas  under  constant  pressure.     This 
law    may  be  stated  as  follows:    Under   constant  pressure  the 
volume  of  a  gas  is  proportional  to  its  absolute  temperature.     The 
law  may  be  written 

v  :vf  =  T:T' 


HEAT  139 

in  which  v  and  v'  represent  the  volumes  and  T  and  T'  the 
corresponding  temperatures  on  the  Absolute  scale. 

Example.  A  mass  of  gas  having  a  volume  of  100  cc.  at  +  20°  C. 
will  have  what  volume  at  —  20°  C.,  the  pressure  remaining  con- 
stant? Solution:  +  20°  C.  =  293°  Abs.  and  -  20°  C.  =  253° 
A  bs.;  hence  we  may  write 

100  :v'  =  293:  253 
v'  =  86.3  cc. 

EXERCISES.  11.  The  volume  of  a  given  mass  of  gas  under  constant 
pressure  at  27°  C.  is  500  cc.  What  will  be  its  volume  at  —  13°  C.? 

12.  A  gas  having  a  volume  of  1000  cc.  at  —  10°  C.  is  heated  and  expands 
under  constant  pressure  to  1200  cc.  Find  the  resulting  temperature. 

CHANGE  OF  STATE 

212.  Fusion  and  the  Melting  Point.  Fusion  or  melting  is 
the  process  by  which  a  solid  changes  to  a  liquid  upon  the  applica- 
tion of  heat.  The  melting  of  ice,  sealing  wax,  glass,  lead,  etc., 
are  all  familiar  examples  of  fusion.  The  temperature  at  which 
melting  occurs  is  called  the  melting  point. 

Many  substances  like  sealing  wax,  wrought  iron,  and  most 
kinds  of  glass  have  no  definite  melting  point.  When  heat  is 
applied  to  such  substances,  they  gradually  soften  to  the  point 
of  liquefaction,  the  change  from  the  solid  to  the  liquid  state  at 
no  instant  being  well  defined. 

Crystalline  substances,  such  as  ice,  sulphur,  cast  iron,  and 
most  crystalline  salts  have  definite  melting  points.  For 
example,  if  a  piece  of  ice  at  —  10°  C.  be  heated,  the  temper- 
ature will  rise  until  it  reaches  0°  C.,  at  which  point  the  ice 
will  melt.  The  change  from  the  solid  to  the  liquid  state,  that 
is,  from  ice  to  water,  is  abrupt,  and  takes  place  at  0°  C.  Like- 
wise, if  water  be  cooled  to  this  temperature,  it  freezes.  The 
freezing  point  and  the  melting  point  are  thus  the  same,  0° 
C.  marking  the  dividing  line  between  the  solid  and  the  liquid 
state. 


140  HIGH  SCHOOL  PHYSICS 

213.  Laws  of  Fusion.     The  principal  facts  relating  to  the 
fusion  or  melting  of  crystalline  solids  may  be  expressed  by  the 
following  laws: 

I.  For  crystalline  substances,  the  freezing  point  and  the  melting 
point  are  the  same. 

II.  Every  crystalline  substance  has  a  definite  melting  point  for 
a  given  pressure. 

III.  When  a  crystalline  substance  reaches  its  melting  point  its 
temperature  remains  constant  until  it  is  entirely  melted.     Thus, 
when  a  piece  of  ice  begins  to  melt,  its  temperature  remains  at 
zero  until  it  is  all  melted,  no  matter  what  the  temperature  of 
the  water  in  which  it  may  be  placed. 

For  Table  of  Melting  Points,  see  Supplement,  601. 

214.  Heat  of  Fusion.     When  a  crystalline  substance  on  being 
heated  reaches  the  melting  point,  its  change  from  the  solid  to 
the  liquid  state  takes  place  without  any  rise  of  temperature. 
This  change,  however,  requires  heat.     This  heat  which  is  con- 
sumed in  changing  the  state  of  a  body  without  changing  its 
temperature  is  called  the  heat  of  fusion,  which  may  be  defined 
as  the  heat  required  to  change  unit  mass  of  a  crystalline  substance 
from  a  solid  to  a  liquid  without  changing  its  temperature. 

The  heat  of  fusion  of  ice  is  80  calories  per  gram.  That  is,  80 
calories  of  heat  are  required  to  change  1  gram  of  ice  at  0°C.  to 
water  at  the  same  temperature. 

215.  Change    of    Volume    during    Fusion.      Substances,    in 
general,  contract  when  they  solidify  and  expand  when  they 
melt.     Thus  if  molten  lead  be  poured  into  a  bullet  mold  and 
there  solidify,  it  will  be  found  that  the  bullet  does  not  quite  fill 
the  mold;    the  lead  contracts  on  solidifying  and  expands  on 
melting.     Certain  highly  crystalline  substances,  on  the  other 
hand,  such  as  ice,  cast  iron,  and  type  metal,  expand  when  they 
solidify  and  contract  when  they  melt.     Such  substances  as  cast 
iron  (Art.  163)  and  type  metal  are  suitable,  therefore,  for  mold- 
ing, since  they  expand  on  solidifying  and  thus  fill  every  part 
of  the  mold  and  reproduce  every  detail  of  the  pattern. 


HEAT 


141 


Experiment.     Pressure 


216.  Water  Expands  on  Freezing.     It  is  estimated  that  917 
cc.  of  water  on  freezing  will  become  1000  cc.  of  ice.     A  cubic 
centimeter  of  ice  is  therefore  lighter  than  a  cubic  centimeter 
of  water,  and  hence  floats.     The  pressure  exerted  by  water  in 
freezing  is  very  great,  as  is  often  illustrated  by  the  freezing  and 
bursting  of  water  pipes  in  winter.     A  cast  iron  bomb  when 
filled  with  water  and  sealed  and  placed  in  a  freezing  mixture  will 
explode  with  a  loud  report.     This  expansion  of  water  in  freezing 
plays  an  important  part  in  the  disintegration  of  rocks  in  the 
formation  of  soil. 

217.  Relation  of  Pressure  to  Fusion, 
applied   to  a  substance  which  con- 
tracts on  melting,  as  ice  for  exam- 
ple, lowers   the  melting  point.     Ice 
may   be  melted    by  applying  a   suf- 
ficiently high  pressure  to  it.      Let  a 
fine  wire  carrying  a  weight  be  passed 
over  a  small  block  of  ice,  as  shown  in 
Fig.  170.     The  ice  just  below  the  wire 
is  melted  by  the  pressure,  the  water 
thus  formed  passing  above  the  wire 
and  freezing  again  on  being  released. 

Thus  in  a  short  time  the  wire  will  cut  its  way  through  the 

ice,  leaving  the  block  as  solid  as  before. 

If  the  temperature  be  near  the  freezing  point,  wet  snow  may 
be  packed  into  "  ice  balls,"  as  every  school- 
boy knows.  Also  two  pieces  of  ice  may  be 
frozen  together  under  warm  water  by  apply- 
ing considerable  pressure  and  then  releasing 
them  suddenly,  Fig.  171. 

218.  Boiling.  If  heat  be  applied  to  a 
kettle  of  water  the  following  facts  may  be 
observed:  (a)  First,  small  bubbles  of  steam 

are   formed  at  the  bottom,  and,  as  they  rise,  condense,  the 

walls  of  the  bubbles  meeting  with  a  sharp  impact  and  thus 


FIG.  170 


FIG.  171 


142  HIGH  SCHOOL  PHYSICS 

giving  rise  to  the  phenomenon  known  as  "  singing."  (b)  When 
the  temperature  of  the  water  rises  sufficiently  high  so  that  the 
vapor  throughout  the  liquid  has  a  pressure  equal  to  or  greater 
than  that  of  the  atmospheric  pressure  upon  the  surface, 
bubbles  form  copiously  at  the  heating  surface  and  rise  to  the 
top  of  the  liquid,  producing  the  agitation  called  boiling,  (c) 
When  the  temperature  reaches  the  boiling  point  it  remains 
constant  until  the  water  all  boils  away. 

Each  liquid  has  a  definite  boiling  point  which  is  constant  for 
constant  pressure. 

For  Table  of  Boiling  Points,  see  Supplement,  602. 

219.  The  Effect  of   Dissolved  Salts  on   the  Boiling  Point. 
Salt  dissolved  in  a  liquid  raises  its  boiling  point.     Most  house- 
wives are  familiar  with  the  fact  that  water  containing  salt  boils 
at  a  higher  temperature  than  that  which  is  pure.     Pure  water 
at  a  pressure  of  one  atmosphere  boils  at  100°C.     If,  however, 
common  table  salt  (NaCl)  be  added  to  the  water  to  the  point 
of  saturation,  the  boiling  point  may  be  raised  to  109°  C. 

220.  Effect  of  Pressure  on  the  Boiling  Point.     The  boiling 
point  of  a  liquid  depends  upon  the  pressure  exerted  upon  it. 
The  bubbles  that  give  rise  to  boiling  cannot  form  in  a  liquid 
unless  they  exert  a  pressure  greater  than  that  of  the  atmosphere. 
Therefore,  if  the  pressure  upon  a  liquid  be  increased,  the  boil- 
ing point  is  raised;    increasing  the  pressure  raises 
the  boiling  point;    decreasing  the  pressure  lowers 
the  boiling  point. 

Experiment.     Put  some  water  at  room  tempera- 
ture and  atmospheric  pressure  into  a  flask,  and  then 
connect   the   flask  to   an   air   pump  (Supplement, 
562),  as  shown  in  Fig.  172.     A  few  strokes  of  the 
FIG  172    pump  will  be  sufficient  to  reduce  the  pressure  so 
that  the  water  will  boil  vigorously.     This  experi- 
ment may  be  performed  in  another  manner  as  follows:  Heat 
the  water  in  a  flask  to  the  boiling  point  and  allow  it  to  cool 
to  60  or  70°  C.,  then  cork  and  invert  the  .flask  as  shown  in 


HEAT 


143 


Fig.  173.  Now  if  water  be  poured  upon  it,  thus  condensing 
the  vapor  in  the  flask  and  thereby  reducing  the  pressure,  the 
water  will  boil. 

In  the  manufacture  of  sugar,  vacuum  pans  are  used  in 
which  the  boiling  point  of  the  syrup 
is  lowered  by  reducing  the  pressure, 
thus  avoiding  the  danger  of  burn- 
ing the-  sugar.  On  the  other  hand, 
in  the  extraction  of  glue  from 
bones,  the  pressure  is  increased 
and  the  boiling  point  of  the  liquid 
correspondingly  raised. 

221.  Relation  of  Altitude  to  Boil- 
ing Point.    Since  atmospheric  pres- 
sure decreases  with  the  elevation, 
the  boiling  point  of  a  liquid  also 
decreases.     The    boiling    point    of 
water  may  therefore  be  used  to  in- 
dicate the  height  of  a  place  above 

the  sea  level.  A  decrease  of  1°  C.  in  the  boiling  point  indi- 
cates an  elevation  of  295  meters,  or  about  968  feet. 

EXERCISE.  13.  The  boiling  point  of  water  at  sea  level  is  100°  C.; 
on  Pike's  Peak  it  is  85.4°  C.  Find  the  elevation  of  Pike's  Peak  above  sea 
level. 

222.  Laws  of  Boiling.     The  facts  with  respect  to  boiling  as 
presented  in  the  preceding  topics  may  be  summarized  briefly 
in  the  following  laws: 

I.  Every  liquid  has  a  definite  boiling  point  which  is  invariable 
under  the  same  conditions. 

II.  An  increase  of  pressure  raises  the  boiling  point;  a  decrease 
of  pressure  lowers  the  boiling  point. 

III.  Salts  dissolved  in  a  liquid  raise  the  boiling  point;  gases 
dissolved  in  a  liquid  lower  the  boiling  point. 

223.  Vaporization.     The    process    by    which    a    substance 


FIG.  173 


144  HIGH   SCHOOL  PHYSICS 

changes  to  a  vapor  is  called  vaporization.  It  may  take  place 
by  boiling,  by  evaporation,  or  by  sublimation. 

Evaporation  is  the  process  by  which  a  liquid  changes  quietly 
at  the,  surface  to  the  vapor  state.  It  takes  place  at  all  tem- 
peratures, even  below  the  freezing  point.  It  has  been  found 
that  a  block  of  ice,  if  left  for  a  few  days  at  a  temperature 
below  zero,  will  lose  considerably  in  weight  by  evaporation; 
clothing  hung  out  to  dry  on  a  cold  winter's  day  will  dry 
though  frozen. 

Sublimation  is  the  process  by  which  a  solid  changes  directly 
to  a  vapor  without  passing  through  the  liquid  state.  If  a  piece 
of  ice,  for  example,  be  placed  under  the  receiver  of  an  air  pump, 
and  the  pressure  be  reduced  to  4  millimeters  or  less,  the  ice  on 
being  heated  will  not  liquefy,  but  will  pass  directly  from  the  solid 
state  to  a  vapor;  that  is,  it  will  sublime.  If  the  pressure  be 
above  4  millimeters,  it  will  liquefy.  Camphor  and  arsenic  will 
sublime  at  atmospheric  pressure.  These  substances  may  be 
liquefied  by  sufficiently  increasing  the  pressure  upon  them. 
Since  arsenic  sublimes  at  atmospheric  pressure  it  is  considered 
detrimental  to  health  to  use  wall  paper  which  contains  any 
considerable  amount  of  arsenic  in  the  coloring  matter. 

224.  Rate  of  Evaporation.  The  rate  at  which  evaporation 
goes  on  depends  upon  four  factors:  (a)  The  extent  of  the  free 
surface  of  the  liquid;  (b)  the  temperature;  (c)  the  pressure 
exerted  upon  the  surface  of  the  liquid;  (d)  the  degree  of  satu- 
ration of  the  space  above  the  liquid. 

It  is  a  familiar  experience  that  if  a  given  quantity  of  water 
be  placed  in  a  broad  shallow  dish  it  will  evaporate  much  more 
quickly  than  if  placed  in  a  deep  narrow  dish;  and  also  that 
the  higher  the  temperature,  the  more  rapid  is  the  rate  of 
evaporation.  The  drying  of  roads  and  streets  after  a  rain 
illustrates  the  effect  of  a  change  of  air  on  the  rate  of  evapora- 
tion. If  after  a  rain  there  be  no  wind,  the  air  soon  becomes 
saturated  and  evaporation  is  retarded;  if,  however,  the  air 
be  in  motion,  evaporation  goes  on  rapidly  and  the  roads 


HEAT  145 

soon  become  dry.  Damp  clothes  hung  out  to  dry  on  a  windy 
day  also  illustrate  the  case  in  point. 

The  rapid  evaporation  of  liquids  in  "  vacuum  pans  "  due  to 
diminished  pressure  is  an  application  of  the  principle  that  the 
rate  of  evaporation  is  increased  by  decreasing  the  pressure. 

225.  Laws    of   Evaporation.     I.     The  rate  of  evaporation  in- 
creases with  the  free  surface  of  the  liquid. 

II.  The  rate  of  evaporation  increases  with  increase  of  tem- 
perature. 

III.  The  rate  of  evaporation  increases  with  a  change  of  air 
in  contact  with  the  liquid. 

IV.  The  rate  of  evaporation  increases  as  the  pressure  dimin- 
ishes. -—•*** 

^^^^rtflP 

226.  Heat  of  Vaporization.     If  heat  be  applied  to  water  the 

temperature  rises  until  it  reaches  the  boiling  point.  Further 
application  of  heat  produces  no  further  rise  of  temperature, 
the  additional  heat  being  used  in  changing  the  water  from  the 
liquid  to  the  vapor  state.  Heat  of  vaporization  is  the  heat 
required  to  change  unit  mass  of  a  substance  from  the  liquid  to  the 
vapor  state  without  'changing  its  temperature.  The  heat  required 
to  change  one  gram  of  water  at  100°  C.  to  steam  at  the  same 
temperature  is  538  calories;  hence  we  say  that  the  heat  of  vapor- 
ization of  water  at  100°  C.  is  538  calories  per  gram.' 

The  high  heat  of  vaporization  of  water  explains  the  value 
of  steam  heat  as  a  means  of  heating  buildings.  Every  gram  of 
steam  that  changes  from  steam  at  100°  C.  to  water  at  the  same 
temperature  gives  up  538  calories  of  heat. 

227.  Vapor  Pressure.     When  a  liquid  evaporates  into  the 
space  above  it,  the  vapor  thus  formed  exerts  a  pressure  which 
is  known  as  the  vapor  pressure  of  the  liquid  at  that  tempera- 
ture.   Each  liquid  has  its  own  definite  vapor  pressure  fpr  a  given 
temperature.     Experiment.     If  a  tube  80  centimeters  in  length 
be  filled  with  mercury  and  inverted  in  a  dish  of  mercury,  Fig. 
174,  a  Torricellian  vacuum,  v,  results.    Now  introduce  into  this 
tube  at  the  bottom,  by  means  of  a  glass  rod  or  pipette,  a  few 


146 


HIGH   SCHOOL   PHYSICS 


drops  of  water,  w,  which  being  lighter  than  the  mercury  rise  in 
the  tube  to  the  surface,  and  a  portion  of  it  evaporates.  The  water 
vapor  thus  liberated  in  the  space  above  the  mercury  exerts  a 
pressure  (the  vapor  pressure  of  water)  which 
forces  the  column  of  mercury  down  to  a  certain 
point,  b.  The  difference  between  the  height  of 
the  column  a  and  that  of  b  represents  in  centi- 
meters the  vapor  pressure  of  water  at  the  given 
temperature.  Now  if  the  tube  be  forced  down 
into  the  mercury  as  shown  in  c,  some  of  the 
vapor  will  liquefy,  but  the  mercurial  column 
will  stand  at  the  same  level  as  before.  The 
vapor  pressure  of  a  liquid  is  the  same  whether 
the  space  above  the  mercury  be  great  or  small, 
provided  there  is  some  free  liquid  present. 

228.  Water  Vapor  in  the  Air.  There  is  in  the 
air  at  all  times  a  certain  amount  of  water  vapor. 
At  20°  C.  (68°  F.)  a  cubic  meter  of  space  when 
saturated  contains  about  17  grams  of  water 
vapor.  The  presence  of  air  in  the  space  does  not  appear  to 
affect  the  amount  of  water  vapor  which  it  can  contain.  That 
is,  a  cubic  meter  of  space  at  20°  C.  will  contain  17  grams  of  water 
vapor,  whether  it  contain  air  at  the  same  time  or  not. 

229.  Humidity.  Humidity  is  a  term  used  to  indicate  the 
quantity  of  water  vapor  in  the  air.  When  the  air  contains  all 
the  water  vapor  it  can  at  a  given  temperature  it  is  said  to  be 
saturated.  At  20°  C.  air  is  saturated  when  it  contains  17  grams 
of  water  vapor  per  cubic  meter. 

Relative  humidity  is  the  ratio  of  the  amount  of  water  vapor 
in  the  air  at  a  given  time  to  the  amount  that  would  be  present 
if  it  were  saturated.  Relative  humidity  is  usually  expressed  in 
terms  of  per  cent;  thus  when  we  say  that  the  relative  humidity 
is  fifty,  we  mean  that  the  air  contains  50  per  cent  of  the  water 
required  to  saturate  it  at  that  temperature. 
For  Humidity  Tables,  see  Supplement,  606. 


FIG.  174 


HEAT  147 

Example.  On  a  given  day  when  the  temperature  was  23°  C. 
it  was  found  that  the  air  contained  14.25  grams  of  water  vapor 
per  cubic  meter.  Find  the  relative  humidity.  Solution:  On 
consulting  the  table  found  in  the  Supplement,  606,  we  find  that  air 
at  23°  C.  is  capable  of  holding  20.355  grams  of  water  vapor  per 
cubic  meter.  The  relative  humidity,  therefore,  is  dtf.-$fs  =  70 
per  cent. 

EXERCISE.  14.  A  given  quantity  of  air  at  20°  C.  contains  10.2  grams 
of  water  vapor  per  cubic  meter.  What  is  the  relative  humidity? 

230.  Relation  of  Humidity  to  Bodily  Comfort.     The  temper- 
ature of  the  human  body  remains  very  nearly  at  a  constant 
temperature  of  98.5°  F.     In  order  to  keep  the  temperature  thus 
uniform,  free  evaporation  from  the  surface  of  the  body  must 
be   maintained.     This   is   especially   true   in   warm   weather. 
Evaporation  is  a  cooling  process;  when  it  goes  on  freely  the 
temperature  is  lowered;    when  it  is  retarded  the  temperature 
rises.     Now  when  the  air  is  filled  with  moisture,  that  is  when 
the  relative  humidity  is  high,  evaporation  is  retarded;    hence 
the  temperature  of  the  body  tends  to  rise.     If  the  air  be  dry, 
that  is,  the  relative  humidity  low,  evaporation  is  accelerated 
and  the  body  remains  cool,  even  though  the  temperature  of 
the  air  be  high.     Men  working  in  the  stoke  hole  of  a  ship 
where  the  temperature  is  very  high  are  able  to  maintain  their 
vigor  because  of  the  fact  that  a  draft  of  air  is  forced  through 
the  room  in  which  they  work,  thus  stimulating  rapid  evapora- 
tion from  their  bodies.      If  the  air  in  the  stoke  hole  were 
allowed  to  become  highly  charged  with  vapor,  it  would  be 
impossible  for  them  to  perform  their  task.     It  has  been  ob- 
served that  the  greatest  number  of  fatalities  due  to  heat  pros- 
trations  in   the   summer   time   occur   not   always   when  the 
temperature  is  highest,  but  on  those  days  when  the  relative 
humidity  is  greatest. 

231.  Humidity  in  Artificially  Heated  Rooms.     Suppose  the 
outdoor  air  in  winter  has  a  temperature  of  0°  C.  and  a  relative 


148 


HIGH   SCHOOL  PHYSICS 


humidity  of  80  per  cent.  Now,  since  a  cubic  meter  of  air  at 
0°  C.  is  capable  of  containing  4.8  grams  of  water  vapor  (Sup- 
plement, 606),  a  humidity  of  80  per  cent  would  represent  T% 
X  4.8  =  3.84  grams  per  cubic  meter.  If  this  air  on  entering 
a  building  be  heated  to  20°  C.  (68°  F.),  each  cubic  meter  will 
be  capable  of  containing  17  grams  of  water  vapor.  Its  rela- 
tive humidity  will  thus  be  lowered  to  ^  =  22.6  per  cent.  For 
health  and  comfort,  however,  air  should  possess  a  relative 
humidity  between  50  and  60  per  cent.  It  is  evident,  there- 
fore, that  unless  some  special  provision  be  made  for  adding 
moisture  to  the  air  when  thus  heated,  the  humidity  will  be  far 
too  low.  All  buildings  heated  by  stoves,  hot  air  furnaces,  or 
steam  radiation  should  have  some  means  of  supplying  to  the 
air  a  sufficient  quantity  of  water  vapor  to  bring  the  humidity 
up  to  the  required  standard.  To  accomplish  this  there  is 
usually  placed  in  connection  with  the  ordinary  furnace  a  water 
pan,  which  should  be  kept  filled  in  order  to  supply  to  the  dry 
warm  air  entering  the  room  a  requisite  amount  of  water 
vapor. 

232.  Dew  Point.  Experiment.  Place  a  thermometer  in  a 
test  tube  partly  filled  with  ether,  Fig.  175.  By  means  of  a 
bent  glass  tube  blow  gently  through  the  liquid  a  stream  of  air 
bubbles  which  will  cause  the  ether  to  evaporate  rapidly,  thus 


FIG.  175 


FIG.  176 


HEAT  149 

producing  a  fall  in  temperature,  as  indicated  by  the  thermom- 
eter. As  the  temperature  falls,  a  point  will  be  reached  at  which 
moisture  or  dew,  condensed  from  the  surrounding  air,  will 
appear  on  the  outside  of  the  tube.  The  temperature  at  which 
this  moisture  appears  is  called  the  dew  point.  The  dew  point 
is  the  temperature  at  which  the  water  vapor  of  the  air  reaches 
saturation  and  begins  to  condense.  Suppose,  for  example,  that 
the  air  on  a  given  day  when  the  temperature  is  20°  C.  con- 
tains 12.7  grams  of  water  vapor  per  cubic  meter.  Now  it 
has  been  found  by  experiment  (Supplement,  606)  that  the 
saturation  temperature  for  12.7  grams  per  cubic  meter  is 
15°  C.  This  means  that  if  the  temperature  of  the  air  fall  to 
15°  C.,  water  will  be  precipitated  in  the  form  of  dew.  In 
other  words,  for  12.7  grams  of  water  vapor  per  cubic  meter, 
15°  C.  marks  the  dew  point.  Fogs,  clouds,  and  rain  result 
from  a  lowering  of  the  temperature  beiow  the  dew  point. 

233.  Distillation.  Distillation  is  a  process  of  separating  one 
liquid  from  another  or  of  separating  a  liquid  from  impurities 
by  heating  the  mixture  in  one  vessel  and  condensing  the  vapor 
in  another.  One  form  of  distilling  apparatus  is  shown  in  Fig. 
176.  Suppose  that  some  water  be  placed  in  the  vessel  S,  called 
the  still,  and  heated.  The  vapor  passes  through  the  coiled 
tube  called  the  worm.  The  vessel  V  is  filled  with  cold  water 
entering  at  a  and  leaving  at  6,  which  condenses  the  vapor  in 
the  coil  c,  from  which  the  pure  water  drops  into  the  receiver 
R.  The  liquid  which  is  collected  in  this  receiver  is  called 
the  distillate. 

By  means  of  this  process  of  distillation  pure  water  may  be 
obtained  from  impure,  and  also  one  liquid  may  be  separated 
from  another,  as  for  example,  commercial  alcohol  from  water, 
in  which  case  alcohol,  being  the  more  volatile,  distils  over  more 
readily  than  the  water.  Mercury  is  often  distilled  in  order 
to  separate  it  from  its  impurities. 


150 


HIGH   SCHOOL   PHYSICS 


COLD  BY  ARTIFICIAL  MEANS 

234.  The  Principle.     The  production  of  cold  by  artificial 
means  is  today  of  great  commercial  importance.     There  are 
three  methods  of  producing  cold  artificially;  namely,   (a)  by 
solution;     (b)  by    evaporation;     (c)  by   expansion    of   gases. 
The  fundamental  principle  involved  in  these  three  methods  is 
the  same;    that  is,  each  process  involves  the  expenditure  of 
energy,  which  in  turn  involves  the  absorption  of  heat.    When, 
for  example,  salt  dissolves  in  a  liquid,  or  a  liquid  evaporates, 
or  a  gas  expands,  energy  in  the  form  of  heat  is  taken  up  and  a 
condition  of  cold  is  produced. 

235.  Cold  by  Solution.     When  a  lump  of  sugar  is  dropped 
into  a  cup  of  coffee,  the  temperature  of  the  coffee  is  lowered 
slightly  as  the  sugar  dissolves,  due  to  the  fact  that  the  dissolv- 
ing of  the  sugar  takes  energy  from  the  liquid  in  the  form  of  heat. 
In  general  the  solution  of  crystalline  substances  in  liquids  tends 
to  lower  the  temperatare,  although  in  some  cases  this  lowering 
of  the  temperature  is  marked  by  secondary  chemical  reactions. 

Experiment.  If  some  salt  (Supplement,  563)  be  put  into  a 
beaker  of  water  at  room  temperature  and  stirred  gently  with  a 
thermometer,  it  will  be  observed  that  the  temperature  of  the 
water  will  fall  several  degrees.  The  dissolving  of  the  salt  takes 
energy  from  the  water  in  the  form  of  heat,  thus  causing  the  fall 
in  temperature. 

236.  The  Ice  Cream  Freezer.     The  common  ice  cream  freezer 

is  one  of  the  best  known  devices  for  produc- 
ing cold  by  artificial  means.     The  principle 
employed  is  that  of  the  production  of  cold 
by    solution.     The    cream   to    be    frozen   is 
placed   in  a  metallic  vessel  A,  Fig.  177,  in 
which  a  stirrer  is  rotated  by   means  of  the 
F      17_         crank  C.     Around  this  vessel  there  is  packed 
a  mixture  of  salt  and  crushed  ice,  B.     The 
contact  of  the  salt  with  the  ice  tends  to  cause  the  latter  to 


HEAT 


151 


melt,  and  the  resulting  liquid  dissolves  the  salt,  both  opera- 
tions requiring  heat,  which  is  withdrawn  from  the  cream  in 
the  vessel  A.  The  object  of  stirring  the  cream  is  to  bring  all 
portions  of  it  successively  in  contact  with  the  walls  of  the  con- 
taining vessel,  causing  it  to  freeze  uniformly.  It  is  important 
to  note  that  the  cream  freezes  when  the  ice  melts;  that  is, 
the  melting  ice  absorbs  heat  which  is  furnished  by  the  cream. 
It  has  been  found  by  experiment  that  the  best  mixture  of  ice 
and  salt  for  producing  a  maximum  lowering  of  temperature  is 
three  parts  of  ice  to  one  part  of  salt  by  weight. 

237.  Cold  by  Evaporation.  Experiment.  When  a  liquid 
evaporates,  energy  in  the  form  of  heat  is  required 
to  separate  the  molecules.  Evaporation  is  there- 
fore a  cooling  process.  If  some  highly  volatile 
liquid,  as  ether,  be  dropped  upon  the  bulb  of 
an  air  thermometer,  Fig.  178,  the  colored  liquid 
in  the  stem  will  quickly  rise,  due  to  the  chill 
produced  by  the  rapid  evaporation  of  the  ether, 
resulting  in  a  contraction  of  the  air  within  the 
bulb.  Sprinkling  the  floor  with  water  in  sum- 
mer cools  the  air  in  the  room  because  of  the 
heat  absorbed  by  the  evaporation  of  the  water. 

Experiment.  Fill  a  small  porous  battery  jar  with  water  and 
place  in  the  vessel  a  thermometer,  Fig.  179,  not- 
ing the  temperature  at  the  beginning  of  the 
experiment.  In  the  course  of  fifteen  minutes 
the  temperature  of  the  water  will  have  fallen 
considerably,  due  to  evaporation  from  the  sides 
of  the  jar.  In  some  warm  countries,  as  Mexico, 
water  is  often  cooled  by  placing  it  in  large  po- 
rous vessels,  which  allow  evaporation  to  take  place 
over  the  entire  surface. 

238.  Cold  by  Expansion.  When  a  gas  expands 
it  does  work  on  the  surrounding  medium;  the  energy  thus 
expended  comes  from  the  gas  in  the  form  of  heat,  and  as  a 


FIG.  178 


FIG.  179 


152 


HIGH   SCHOOL   PHYSICS 


FIG.  180 
Carbon  Dioxide  Snow 


result  the  temperature  is  lowered.  The  cooling  effect  of  an 
expanding  gas  may  be  strikingly  illustrated  in  the  following 
manner.  Obtain  a  tank  of  liquid  carbon  dioxide,  such  as  is 

employed  in  connection  with  soda 
fountains.  The  carbon  dioxide  in 
the  tank  is  under  enormous  pres- 
sure. If  now  the  stop  cock  con- 
nected with  the  tank  be  opened 
and  the  gas  within  be  allowed  to 
expand,  there  will  result  a  lowering 
of  the  temperature  due  both  to  the 
vaporization  of  the  liquid  and  the 
expansion  of  the  gas.  The  chill  produced  is  sufficient  to 
freeze  the  carbon  dioxide,  which  appears  in  the  form  of  a 
white  mist  or  snow,  Fig.  180. 

239.  The  Ice  Machine.     The  principle  of  the  ice  machine 
may  be  illustrated  by  means  of  a  very   simple 
apparatus,  as  shown  in  Fig.  180.     Two  tanks  A 

and  B  are  connected  by  means  of  a  short  tube. 
Tank  A,  which  contains  some  liquid  ammonia, 
is  placed  in  the  water  to  be  frozen;  the  pis- 
ton in  tank  B  is  suddenly  withdrawn,  thus  re- 
ducing the  pressure.  The  liquid  ammonia  in 
A  evaporates  and  expands  into  B,  producing  a 
chill,  and  thus  tending  to  freeze  the  water 
in  C.  The  lowering  of  the  temperature  is  pro- 
duced by  both  the  evaporation  and  expansion 
of  the  ammonia.  In  actual  practice  the  machine 
is  very  much  more  complicated  than  that  shown  in  Fig.  181. 
(Supplement,  564.) 

TRANSMISSION  OF  HEAT 

240.  Modes   of  Transmission.     Heat  may  be  transmitted 
from  one  point  to  another  in  three  ways:  (a)  by  conduction, 
(b)  by  convection,  and  (c)  by  radiation. 


B 


FIG.  181 


HEAT  153 

Conduction  is  the  transmission  of  heat  through  a  body  from 
molecule  to  molecule,  as  in  the  heating  of  a  piece  of  iron  in  a 
flame.  The  heat  is  transmitted  from  one  end  of  the  iron  to  the 
other  by  conduction. 

Convection  is  the  transmission  of  heat  by  means  of  a  current, 
as  for  example,  winds  and  ocean  currents.  The  Gulf  Stream 
is  an  example  of  a  convection  current. 

Radiation  is  a  transfer  of  energy  through  space  by  means  of 
waves  set  up  in  a  hypothetical  medium  called  the  ether.  The 
earth  is  thus  heated  by  radiation  from  the  sun. 

241.  Conductivity  of  Solids.     Experiment.     If  one  end  of  a 
piece  of  wire  be  held  in  a  Bunsen  burner,  the  heat  is  rapidly 
transmitted  along  the  wire,  which  will  soon  become  too  hot  to 
hold.     Metals  are  in  general  good  conductors.     If  now  a  glass 
rod  be  held  in  a  flame  as  in  the  case  of  the  wire,  it  will  be  found 
that  the  glass  may  be  entirely  melted  only  a  few  centimeters 
from  the  hand  without  the  rod  becoming  too  hot  to  hold.     Glass 
is  a  poor  conductor  of  heat.     Again,  a  match  may  be  burned 
until  the  flame  almost  touches  the  fingers,  showing  that  wood 
is  a  very  poor  conductor  of  heat. 

242.  Relative   Conductivity  of  Wood  and   Metal.     Experi- 
ment.    The  relative  conductivity  of  wood  and  metal  may  be 
shown  by  wrapping  a  piece  of  paper 

around  a  cylinder,  Fig.  182,  one  end 
of  which  is  composed  of  metal  and 
the  other  of  wood.  If  now  the  cyl- 
inder be  held  in  a  flame,  the  paper 
will  char  where  it  toughes  the  wood, 
but  will  not  be  burned  where  it  is 
in  contact  with  the  metal,  due  to 
the  fact  that  the  metal  conducts 
the  heat  away  so  rapidly  as  to  keep 

*  x1  IG.  loJ 

the  paper  below  the  burning  point. 

243.  Conductivity  of  Wire  Gauze.     Experiment.     If  a  piece 
of  wire  gauze  be  held  over  a  small  flame,  Fig.  183,  the  flame  will 


154  HIGH   SCHOOL   PHYSICS 

not  pass  through  it.  Also,  if  the  gauze  be  placed  a  short  dis- 
tance above  the  burner  and  the  gas  turned  on  and  lighted  above 
the  gauze,  the  flame  will  refuse  to  pass  down  to  the  burner.  The 
metallic  gauze  conducts  the  heat  away  from  the  flame  so  rapidly 
that  the  gas  on  the  opposite  side  in  each  case  is  not  heated  to 
the  point  of  combustion. 

This  property  of  wire  gauze  is  made  use  of  in  the  construction 
of  the  Davy  Lamp,  Fig.  184,  named   after  its  inventor,  Sir 


FIG.  183  FIG.  184 

Humphrey  Davy.  This  device,  which  is  often  used  by  miners, 
consists  of  a  small  oil  lamp,  the  flame  of  which  is  covered  by 
a  cylinder  of  wire  gauze.  While  any  inflammable  gas  encoun- 
tered in  the  mine  may  pass  freely  through  the  gauze  and  burn 
quietly  within,  the  flame  cannot  pass  outward  and  so  cause  an 
explosion. 

244.  Conductivity  of  Liquids.  Liquids  are  poor  conductors 
of  heat,  the  conductivity  of  water,  for  example,  being  only 
about  TuW  that  of  silver,  which  is  sometimes  taken  as  a  stand- 
ard for  the  conductivity  of  metals. 

Experiment.  Fasten  a  piece  of  ice  in  the  bottom  of  a  test 
tube  nearly  full  of  water.  Hold  the  upper  part  of  the  tube  in 
a  flame,  Fig.  185.  In  a  short  time  the  water  in  the  top  of  the 
tube  will  begin  to  boil,  thus  giving  boiling  water,  tepid  water, 
and  ice  water  all  in  the  same  vessel. 

Experiment.     The  nonconducting  property  of  water  may  be 


HEAT 


155 


very  well  illustrated  by  means  of  an  apparatus  shown  in  Fig. 
186.  An  air  thermometer  is  sealed  into  the  stem  of  a  funnel, 
which  is  then  filled  with  water  to  within  a  few  centimeters  of 
the  surface.  Some  ether  is  poured  upon  the  surface  of  the 
water  and  is  then  set  on  fire.  Notwithstanding  the  fact  that 
the  ether  burns  only  a  few  millimeters  above  the  bulb  of  the 
air  thermometer,  it  will  be  observed  that  the  colored  liquid  in 
the  stem  is  not  affected  thereby,  thus  showing  that  practically 
no  heat  is  conducted  down  through  the  water. 


FIG.  185 


FIG.  186 


245.  Conductivity    of    Gases.     Gases    are    extremely    poor 
conductors  of  heat.     Woolen  clothing  owes  its  nonconducting 
properties  partly  to  the  fact  that  the  wool  fibre  is  a  poor  con- 
ductor, but  more  largely  because  of  the  nonconducting  property 
of  the  air  enclosed  within  it.     The  fur  of  animals  is  an  effec- 
tive protection  from  cold  for  the  same  reason.    The  air  spaces 
between  double  windows  and  between  the  walls   of   houses 
are  also  illustrations  of  some  of  the  uses  made  of  the  noncon- 
ducting properties  of  gases. 

246.  The  Fireless  Cooker.     Of  recent  years  much  use  has 
been  made  of  the  principle  of  the  nonconducting  properties  of 
gases  in  the  construction  of  the  so-called  fireless  cooker,  Fig. 


156 


HIGH  SCHOOL  PHYSICS 


FIG.  187 


187.  This  device  consists  usually  of  a  wooden  box  contain- 
ing a  number  of  receptacles  designed  to  receive  the  food  to 
be  cooked.  Around  these  vessels  there  is  closely  packed  some 
material,  such  as  hay,  felt,  asbestos,  or 
other  nonconducting  material,  which 
encloses  within  its  interstices  noncon- 
ducting air.  The  food  to  be  cooked  is 
heated  to  the  boiling  point  and  then 
placed  in  the  receptacles  within  the 
cooker  and  carefully  covered.  Due  to 
the  nonconducting  property  of  the  pack- 
ing material,  and  especially  to  the  air 

enclosed  within  its  spaces,  sufficient  heat  is  retained  in  the 
food  until  it  is  cooked.  The  efficiency  of  the  apparatus  de- 
pends, of  course,  upon  the  retention  of  the  heat  imparted  to 
the  food  before  it  is  placed  in  the  cooker. 

247.  The  Thermos  Bottle.    A  Dewar  flask  is  a  double  walled 
glass  vessel,  Fig.  188,  the  space  between  the  walls  being  an 
extremely  low  vacuum.     Only  a  very  small  heat 
exchange,  therefore,  takes  place  by  conduction  be- 
tween the  inside  and  the   outside  of   the  vessel. 

Liquids  with  low  boiling  points  such  as  liquid  air 
or  liquid  oxygen  may  be  kept  much  longer  in 
Dewar  flasks  than  in  ordinary  vessels.  Recently 
such  flasks  enclosed  in  an  outer  covering  of  leather 
or  metal  have  been  placed  upon  the  market  under 
the  name  of  " thermos"  bottles,  which  serve  equally 
well  for  keeping  a  liquid  hot  or  cold.  The  noncon- 
ducting property  of  these  vessels  is  due  to  the  low  vacuum 
between  the  double  walls. 

248.  Convection.     Convection  is  the  transmission  of  heat  by 
currents.     An  example  of  convection  currents  may  be  seen  in 
the  motion  of  water  in  a  beaker  when  heated  as  shown  in  Fig. 
189.     Currents  of  hot  air  rising  from  radiators  or  furnaces  are 
also  convection  currents. 


FIG.  188 
Dewar 
Flask 


HEAT 


157 


FIG.  189 


An  explanation  of  convection  may  be  given  somewhat  as 
follows:   When  a  given  mass  of  a  fluid,  air  or  water,  is  heated, 
it  expands  and  its  density  diminishes.    The  sur- 
rounding medium  being  the  heavier,  tends,  there- 
fore, to  displace  the  warm  and  relatively  light 
fluid,  forcing  it  upward.     As  the  warm  current 
rises  it  carries  heat  with  it.     Thus  it  appears 
that  a  fluid  which  is  heated  does  not  rise  of  its 
own  accord,  but  is  forced  upward  by  the  colder 
and  heavier  medium  surrounding  it. 

249.  Use  of  Convection  Currents  in  Heating.  Experiment, 
Convection  currents  such  as  are  used  in  hot  water  heating  sys- 
tems may  be  demonstrated  by  a  simple  device, 
such  as  is  shown  in  Fig.  190.  Fill  the  flask  and 
tubes  with  water.  Then  add  to  the  open  vessel 
at  the  top,  some  colored  liquid.  Now  when  heat 
is  applied  to  the  lower  vessel  the  cold  water  in 
the  tube  descends  and  the  hot  water  rises,  thus 
giving  rise  to  convection  currents,  the  colored 
liquid  showing  very  clearly  their  direction.  The 
lower  vessel  corresponds  to  the  furnace,  the  tubes 
to  the  pipes  and  coils  of  the  heating  system,  and 
the  upper  vessel  to  the  expansion  tank,  which  is 
usually  located  in  an  upper  story  of  the  house. 
In  Fig.  191  there  is  shown  a  hot. water  heating 
system,  and  in  Fig.  192  a  hot  water  tank  such  as 


FIG.  190 


is  used  in  connection  with  the  ordinary  furnace  to  provide  hot 
water  throughout  the  house. 

250.  Ventilation.  Experiment.  The  fundamental  principles 
governing  ventilation  may  be  illustrated  by  an  experiment 
with  a  candle  and  a  glass  flask,  Fig.  193.  By  means  of  a  wire 
lower  a  small  lighted  candle  into  a  flask  having  a  rather  wide 
neck.  The  flame  burns  brightly  for  a  while,  and  then  begins 
to  grow  dim,  and  soon  goes  out,  due  to  the  fact  that  the  oxygen 
of  the  air  within  the  flask  is  burned  out.  Now  if  a  strip  of 


158 


HIGH   SCHOOL  PHYSICS 


tin  or  cardboard  be  thrust  down  into  the  neck  of  the  flask 
and  be  so  adjusted  that  a  stream  of  cool  air  will  descend  on 
one  side  and  a  stream  of  hot  air  ascend  on  the  other,  Fig.  194, 

Hot  < 


Hot 


FIG.  191 


FIG.  192 

we  shall  have  the  condition  necessary 
for  the  ventilation  of  the  flask  and  the 
candle  flame  will  then  burn  brightly. 

Ventilation  is  the  process  by  which 
fresh  pure  air  is  supplied  to  rooms  and 
buildings  and  impure  air  removed. 

251.  The  Constituents  of  the  Air.  In 
order  to  discuss  intelligently  the  subject 


of  ventilation  it  will  be  necessary  to  consider  briefly  the  com- 
position of  the  air,  and  also  the  question  of  what  consti- 
tutes pure  and  impure  air.  Air  is  composed  of  two  gases, 
oxygen  (O)  and  nitrogen  (N),  in  the  ratio  of  1  to  4  by  vol- 
ume. In  addition  to  oxygen  and  nitrogen,  the  air  contains 
also  a  small  proportion  of  a  number  of  other  substances, 


HEAT 


159 


such   as   water   vapor,    ozone,    carbon   dioxide,   smoke,   dust, 
germs,  etc. 

Oxygen  is  the  life-giving  principle  of  the  air.  It  supports 
combustion,  whether  it  be  in  the  case  of  a  candle  flame,  the 
burning  of  wood  in  a  grate,  coal  in  a  furnace,  or  the  combus- 
tion of  the  waste  tissues  of  the  body.  Nitrogen  is  an  inert 
gas  which  serves  to  dilute  the  oxygen  and  thus  prevent  too 
rapid  combustion.  If  the  air  consisted  of  pure  oxygen,  com- 
bustion would  go  on  at  a  destructive  rate.  It  can  be  shown 
that  in  undiluted  oxygen  even  iron  will  burn,  Fig.  195.  Carbon 


FIG.  193 


FIG.  194 


FIG.  195. 


dioxide  is  a  non-poisonous  gas  and  a  non-supporter  of  animal 
life  and  combustion.  If  one  were  placed  in  a  tank  filled  with 
carbon  dioxide  he  would  be  smothered  as  effectively  as  if  he  were 
drowned  in  water.  While  carbon  dioxide  is  not  in  itself  poison- 
ous, yet  it  is  usually  taken  as  the  measure  of  the  impurities 
present  in  the  air  of  a  room  due  to  respiration  and  other  exha- 
lations from  the  body.  If  there  be  a  relatively  large  quantity 
of  carbon  dioxide  present  in  a  room,  it  is  assumed  that  the  air 
is  impure. 

Pure  air  is  air  which  is  free  from  injurious  gases  or  vapors, 
dust,  and  disease  germs. 

252.  Test  for  Carbon  Dioxide.  Experiment.  That  carbon 
dioxide  is  given  off  from  the  lungs  in  respiration  may  be  shown 


160  HIGH   SCHOOL  PHYSICS 

by  forcing  some  air  from  the  lungs  through  a  small  glass  tube 
into  clear  lime  water  contained  in  a  test  tube.  When  the  car- 
bon dioxide  comes  in  contact  with  the  lime  water  a  white 
precipitate  of  calcium  carbonate  (CaCOa)  is  formed.  (Sup- 
plement, 565.)  The  degree  of  turbidity  or  milkiness  of  the 
lime  water  is  taken  as  a  test  of  the  quantity  of  carbon  dioxide 
present. 

253.  The    Object    of    Ventilation.     It   is    quite    commonly 
believed  that  the  main  object  of  ventilation  is  to  furnish  a  fresh 
supply  of  oxygen  and  to  eliminate  the  carbon  dioxide.    Experi- 
ments have  shown,  however,  that  unless  the  oxygen  fall  below 
12  per  cent  and  the  carbon  dioxide  rise  above  3  per  cent,  condi- 
tions which  very  rarely  occur  in  human  habitations,  no  marked 
discomfort  ensues  from  the  deficiency   of   oxygen  or   excess 
of  carbon  dioxide.     The  fact  remains,  however,  that  unless  the 
air  in  a  room  be  frequently  changed,  the  healthy  tone  of  the  hu- 
man body  cannot  be  maintained.     This  seems,  then,  that  the 
ill  effects  which  arise  from  the  breathing  of  vitiated  air  comes 
not  so  much  from  a  deficiency  of  oxygen  or  an  excess  of  car- 
bon dioxide  as  from  other  causes,  such  as  the  presence  of 
injurious    gases,  infectious    germs,    faulty    temperature,   and 
moisture  regulation,  etc.     We  ventilate,  then,  to  supply  fresh 
out-of-door  air,  and  to  remove  impure  air,  and  also  to  regulate 
temperature  and  moisture  conditions. 

It  is  important  -to  make  a  distinction  between  danger  and 
comfort  in  the  air  conditions  of  a  room.  For  example,  a  room 
cannot  long  remain  comfortable  that  does  not  have  some  degree 
of  ventilation;  that  is,  it  may  be  too  hot  or  too  cold,  too  dry 
or  too  moist. 

It  is  estimated  that  the  proper  quantity  of  air  that  should 
be  supplied  to  a  room  is  about  2000  cubic  feet  per  person  per 
hour. 

254.  Means  of  Securing  Ventilation.     Natural  ventilation 
is  that  which  takes  place  through  the  walls,  cracks  around 
doors,  windows,  etc.,  and  through  the  opening  and  closing  of 


HEAT 


161 


doors  in  passing  from  one  room  to  another,  Fig.  196.  Except 
on  windy  days  this  method  is  not  sufficient  to  keep  the  air 
of  most  rooms  in  proper  condition  for  breathing,  and  espe- 
cially is  this  true  of  rooms  where 
large  numbers  of  persons  are  con- 
gregated. 

That  a  passage  of  air  from  room 
to  room  does  actually  take  place 
may  often  be  demonstrated,  as 
shown  in  Fig.  197,  by  means  of  a 
candle  flame.  At  the  top  of  the 
door  the  flame  is  bent  in  one  di- 
rection, at  the  bottom  in  another 
direction,  thus  showing  that  there  is  a  draft  of  air  into  the 
room  at  the  bottom  and  a  draft  out  at  the  top. 

Ventilation  by  means  of  hot  air  furnaces,  in  which  pure  out- 
of-door  air  is  heated  and  then  passed  into  the  rooms  through 


FIG.  196 


FIG.  197.  —  Inflow  and  Outflow  of 
Air  through  Open  Door 


FIG.  198 


registers,  is  a  very  good  method  of  ventilating  buildings  which 
are  not  too  large,  Fig.  198.     In  large  buildings,  such  as  audi- 


162 


HIGH   SCHOOL   PHYSICS 


toriums,  the  most  economical  and  efficient  method  of  changing 
the  air  is  by  means  of  mechanically  driven  fans,  Fig.  199. 

255.  Radiation.  Radiation  has  already  been  denned  (Art. 
240)  as  the  transmission  of  energy  by  means  of  ether  waves. 
All  space  is  supposed  to  be  filled  with  a  medium  called  ether, 
which  is  assumed  to  have  the  properties  of  transmitting 
energy  by  means  of  waves.  This  so-called  radiant  energy 

may  be  focused  by  means 
of  a  lens,  Fig.  200.  If  a 
lens,  such  for  example  as 
a  common  reading  glass,  be 


\ 


FIG.  199 


FIG.  200.  —  Burning  Glass 


held  in  the  sun's  rays,  they  will  be  brought  to  a  focus  in  which 
a  piece  of  paper  may  readily  be  set  on  fire.  It  is  important  to 
note  in  this  connection  that  in  the  transmission  of  energy  from 
the  sun  to  the  earth  the  intervening  space  is  not  heated,  and  there- 
fore we  cannot  properly  speak  of  this  radiant  energy  as  heat.  It 
is  true  that  the  waves  by  means  of  which  the  energy  is  trans- 
mitted may  have  their  origin  in  a  heated  body,  the  sun,  and 
when  they  fall  upon  the  earth  they  may  give  rise  to  heat, 
which  is  transmitted  from  point  to  point  through  the  medium 
of  matter  by  conduction  or  convection.  It  must  not  be 
thought,  however,  that  the  sun  is  the  only  source  of  radiant 
energy.  All  hot  bodies  may  lose  heat  by  conduction,  convec- 


HEAT  163 

tion,  and  radiation.  The  important  point  to  be  kept  in  mind  is 
that  radiation  is  a  transference  of  energy,  which  when  expended 
upon  matter  may  give  rise  to  heat. 

256.  Transmission  and  Absorption  of  Radiant  Energy. 
Some  substances  allow  radiant  energy  to  pass  through  readily. 
Rock  salt,  for  example,  transmits  radiant  energy  the  most 
readily  of  any  substance  known.  Other  substances  do  not 
transmit  radiant  energy  readily,  but  absorb  it.  Lampblack 
absorbs  radiant  energy  to  a  greater  degree  than  any  other  sub- 
stance known. 

Radiant  energy,  as  has  been  stated,  is  assumed  to  be  trans- 
mitted by  means  of  ether  waves,  some  of  which  are  long  and 
some  short.  Some  substances  like  glass  and  water  allow  the 
short  waves  to  pass  through  readily,  but  absorb  the  long 
waves.  Radiant  energy  comes  from  the  sun  to  the  earth  in 
the  form  of  both  long  waves  and  short  waves.  Now  the  at- 
mosphere surrounding  the  earth  contains  enormous  quantities 
of  water  vapor,  which  transmits  the  short  waves  and  shuts  off 
the  long  waves.  These  short  waves  on  striking  the  earth  heat 
it,  and  then  give  rise  to  long  waves,  which  are  prevented  by 
the  water  vapor  in  the  atmosphere  from  passing  out  into 
space.  Thus  the  water  of  the  atmosphere  serves  as  a  sort 
of  protecting  blanket,  which  by  shutting  out  the  long  waves 
keeps  our  days  from  being  excessively  hot,  and,  by  preventing 
too  rapid  radiation,  keeps  our  nights  from  being  excessively 
cool. 

The  hot  house  has  been  called,  and  quite  rightly,  a  trap  to 
catch  sunbeams.  The  short  waves  of  radiant  energy  pass  read- 
ily through  the  glass,  and  falling  upon  the  interior  heat  it.  Now 
the  heat  thus  generated  gives  rise  to  long  waves  which  can- 
not pass  through  the  glass,  their  energy  being  thus  entrapped, 
so  to  speak.  That  glass  allows  short  waves  to  pass  and  not 
long  waves  may  be  seen  when  we  consider  the  fact  that  the  short 
waves  conveying  radiant  energy  from  the  sun  pass  readily 
through  the  glass  of  windows,  and  falling  on  our  bodies  give 


164 


HIGH  SCHOOL  PHYSICS 


rise  to  heat.  On  the  other  hand  it  is  a  well  known  fact  that  if 
a  glass  screen  be  placed  in  front  of  a  grate  fire  it  will  effectively 
shut  off  the  heat ;  that  is,  it  will  prevent  the  transmission  of 
the  long  waves  conveying  radiant  energy  from  the  fire. 

257.  Illustrations  of  the  Absorbing  Power  of  Lampblack. 
Experiment.  To  show  that  lampblack  absorbs  radiant  energy 
to  a  greater  degree  than  does  glass,  take  two  air  thermom- 
eters as  shown  in  Fig.  201  (Supplement,  566)  and  coat  the  bulb 
of  one  of  them  with  lampblack  from  a  candle  flame.  Adjust 
the  colored  liquid  to  about  the  same  height  in  both  stems. 
Now  place  a  hot  body  such  as  a  Bunsen  flame  or  a  sheet  of  hot 
iron  midway  between  the  bulbs.  The  radiation  from  the  hot 
body  passes  quite  readily  through  the  glass  bulb,  but  is  absorbed 

by  the  blackened  bulb,  as  is  shown 
by  the  lowering  of  the  colored 
liquid  in  the  tube. 


FIG.  201 


FIG.  202 


258.  Absorption  and  Reflection  of  Radiant  Energy.  The 
amount  of  radiant  energy  absorbed  or  reflected  by  a  body 
depends  upon  (a)  the  temperature  of  the  body  and  (b)  the 
nature  of  its  surface.  In  general  a  rough  black  body  is  a  good 
absorber  but  a  poor  reflector  of  radiant  energy;  a  smooth 
bright  body  is  a  poor  absorber  but  a  good  reflector. 

Experiment.  To  determine  the  relative  radiating  power  of 
a  black  body  as  compared  with  that  of  a  bright  body.  Take 


HEAT  165 

two  bright  tin  .cans  (baking  powder  cans  from  which  the  wrap- 
pings have  been  removed  will  do)  and  punch  a  hole  in  the  cover 
of  each  for  the  admission  of  the  thermometers,  Fig.  202.  Coat 
one  of  the  cans  heavily  with  lampblack.  Fill  both  with  hot 
water  and  note  the  temperature  of  each  at  the  beginning  of 
the  experiment.  After  a  time  again  observe  the  temperature 
of  the  water  in  each  can.  It  will  be  found  that  the  water  in 
the  black  can  is  considerably  cooler  than  that  in  the  bright 
one.  A  rough  black  body  radiates  more  readily  than  a  smooth 
bright  body. 

Experiment.  Again  fill  both  cans  with  cold  water  and  insert 
the  thermometers.  Place  the  cans  in  the  sunshine,  or  at  equal 
distances  from  a  radiator.  Note  the  temperature  at  the  begin- 
ning of  the  experiment  and  at  the  end  of  half  an  hour.  The 
water  in  the  black  can  will  be  the  hotter  by  several  degrees. 
A  rough  black  body  is  a  better  absorber  of  heat  than  is  a 
bright  polished  body. 

EXERCISES.  15.  If  a  piece  of  black  cloth  and  a  piece  of  white  cloth  be 
placed  in  the  sunshine  upon  the  surface  of  snow  in  winter,  which  will  settle 
into  the  snow  the  more  rapidly? 

16.  Should  cans  used  in  shipping  milk  in  summer  be  bright  or  dark 
in  color,  and  why? 

17.  Which  is  the  warmer  in  winter,  a  shoe  that  is  polished  or  one  that 
is  not  polished,  other  things  being  equal? 

RELATION  OF  HEAT  TO  WORK 

259.  Joule's  Experiment.  The  first  accurate  determination 
of  the  relation  between  heat  and  work  was  made  in  1845  by 
Joule  (1818  —  1889),  an  English  physicist.  His  experiment 
was  conducted  somewhat  as  follows.  A  given  quantity 
of  water  was  placed  in  a  vessel  containing  a  paddle  wheel, 
Fig.  203.  About  the  axle  of  the  wheel  there  was  wound  a 
strong  flexible  cord,  to  the  end  of  which  was  attached  a  weight 
w.  When  the  weight  was  allowed  to  fall,  the  work  done,  meas- 
ured in  foot  pounds,  was  equal  to  the  weight  w  in  pounds 


166 


HIGH   SCHOOL  PHYSICS 


times  the  space  s.  The  falling  of  the  weight  caused  the 
paddles  to  rotate,  thus  doing  the  work  upon  the  water  and 
causing  a  rise  in  temperature.  Joule's  experiment  demon- 
strated that  a  weight  of  77.2 
pounds  falling  through  a  dis- 
tance of  10  feet  (772  F.P.)  would 
raise  the  temperature  of  1  pound 
of  water  1°  F.  This  means  that 
a  pint  of  water  (1  pound)  in 
cooling  from  the  boiling  point 
(212°  F.)  to  room  temperature 
(70°  F.)  would  give  out  heat 
enough  to  do  more  than  100,000 
foot  pounds  of  work. 

260.  The  Mechanical  Equiv- 
alent of  Heat.  The  relation  of 
work  units  to  heat  units  is  called 
the  mechanical  equivalent  of  heat. 
In  1879  Professor  Rowland  of 
Johns  Hopkins  University  made 
a  series  of  classical  experiments 

*-  with     an     improved     form    of 

Joule's  apparatus,  which  determined  the  following  values  for 
the  mechanical  equivalent  of  heat: 

1    calorie  =  4.19  X  107  ergs 
1  B.T.U.  =  778  foot  pounds 

261.  Heat  of  Combustion.  The  heat  of  combustion  of  a 
substance  is  measured  by  the  number  of  units  of  heat  given 
out  when  unit  quantity  of  the  substance  is  burned.  The  heat 
of  combustion  of  fuel  such  as  coal  and  illuminating  gas  may 
be  expressed  in  calories  or  in  British  thermal  units  (B.T.U.). 
It  has  been  shown  by  experiment  that  the  heat  of  combustion 
for  coal  of  average  grade  and  illuminating  gas  are '  about  as 
follows: 


HEAT 


167 


1  pound  coal  =  15,000  B.T.U. 
\  cubic  foot  illuminating  gas  =  600  B.T.U. 

Coal  is  classified,  with  reference  to  the  volatile  matter  that  it 
contains,  into  bituminous  or  soft  coal,  semi-bituminous,  and 
anthracite  or  hard  coal,  (a)  A  bituminous  coal  is  one  that 
contains  over  20  per  cent  of  volatile  matter.  This  coal  is  used 
largely  in  the  manufacture  of  gas.  Hocking  Valley  coal  is  a 
type  of  bituminous  coal  of  average  grade  having  a  heat  of 
combustion  of  about  14,000  B.T.U.  per  pound,  (b)  Semi- 
bituminous  coal  looks  something  like  anthracite,  but  is  lighter 
in  weight  and  burns  more  readily.  It  is  valuable  where  it 
is  necessary  to  keep  an  intense  heat.  A  high  grade  semi- 
bituminous  is  that  known  as  Pocahontas,  the  heat  of  combus- 
tion of  which  is  15,700  B.T.U.  per  pound,  (c)  Anthracite  or 
hard  coal  contains  less  than  10  per  cent  of  volatile  matter. 
It  ignites  very  slowly  and  burns  at  a  high  temperature.  Owing 
to  its  smokeless  burning  it  is  used  almost  altogether  for  domes- 
tic purposes.  A  good  quality  of  anthracite  coal,  such  as  Scran- 
ton  coal,  has  a  heat  of  combustion  of  about  13,800  B.T.U. 
per  pound. 

For  Table  of  Heats  of  Combustion,  see  Supplement,  608. 

262.  The  Heat  Engine.  The  usual  method  of  transforming 
heat  into  mechanical  work  is 
by  means  of  the  heat  engine, 
as  is  illustrated  by  the  steam 
engine  of  the  railroad  locomo- 
tive and  the  gas  engine  of  the 
automobile.  In  the  ordinary 
form  of  the  steam  engine,  Fig. 
204,  steam  under  high  pres- 
sure is  admitted  to  the  cylin-  FlG  2Q4 
der  C,  Fig.  205,  first  on  one 

side  and  then  on  the  other  of  the  piston  P,  causing  it  to  move 
back  and  forth  from  a  to  b.     The  admission  of  the  steam  to 


168 


HIGH  SCHOOL  PHYSICS 


the  cylinder  C  is  regulated  by  the  sliding  valve  S,  which 
admits  live  steam  to  one  side  of  the  cylinder  and  allows  the 
exhaust  or  dead  steam  to  escape  on  the  other  side.  The 

motion  of  the  valve  S  and  that  of 
the  piston  P  are  in  opposite  direc- 
tions. (Supplement,  567.) 

263.  The   Gas  Engine.     In  the 
gas  engine  an  explosive  mixture  of 
air  and  gas  or  gasoline  is  admitted 
to   the   cylinder   C,  Fig.  206,  and 
exploded  by  means  of  an  electric 
spark.     The  explosion  of  the  gas 
gives  rise  to  a  sudden  expansion 
which  causes  the  piston  to  move. 
The  inertia  of  the  flywheel  carries 
the  piston  back  to  the  upper  end 
of  the  cylinder,  where  an  explosion 
of    the   confined   gas   again  takes 
place,   these    explosions    being    so 
timed  as  always  to  occur  when  the 
piston  is  in  the  position  shown  in 
the  figure.     The  waste  or  exploded 
gas  is  discharged  from  the  cylinder 
through  the  valve  vf  between  ex- 
plosions.    (Supplement,  568.) 

264.  Efficiency.    The  efficiency  of 
any  piece  of  heat  apparatus,  whether 
it  be  a  steam  engine,  a  furnace,  or  an 

ordinary  gas  burner  under  a  kettle,  is  the  ratio  of  the  useful  energy 
gotten  out  to  the  total  heat  energy  put  in ;  that  is, 

useful  energy  out 
efficiency  =  ^—  ^— 

heat  energy  in 

The  efficiency  of  the  ordinary  locomotive  is  about  3  to  4  per 
cent,  which  means  that  for  every  hundred  per  cent  of  energy 


FIG.  205 


HEAT 


169 


put  into  it  in  the  form  of  coal  we  get  in  return  only  about  3  to 
4  per  cent  in  the  form  of  useful  work.  Considering  the  losses 
in  both  engine  and  boiler,  that  is,  "from  coal 
bin  to  flywheel,"  the  efficiency  of  the  modern 
stationary  engine  is  about  8  to  12  per  cent. 

Example.  One  cubic  foot  of  gas  is  burned 
under  a  kettle  containing  a  gallon  (8  pounds) 
of  water.  The  temperature  of  the  water  is 
changed  from  68°  to  110°  F.  Find  the  effi- 
ciency of  the  burner  and  kettle.  Solution : 
1  cubic  foot  of  gas  gives  600  B.T.U.  of  heat. 
To  change  8  pounds  of  water  from  68°  to  110°  F. 
requires  8  X  42  =  336  B.  T.  U.  Efficiency  =  use- 
ful energy  out  /heat  in  =  336/600  =  56  per  cent. 

EXERCISES.    18.   A  gallon  of  water  (8  Ibs.)  is  heated 
in  a  kettle  on  a  gas  range  from  room  temperature 
(70°  F.)  to  the  boiling  point  (212°  F.).     How  many          FIG>  206 
B.T.U.  go  into  the  water? 

19.  If  the  efficiency  of  the  burner  and  kettle  (exercise  18)  is  50  per 
cent,  how  many  cubic  feet  of  gas  were  consumed,  assuming  each  cubic 
foot  of  gas  to  furnish  600  B.T.U.? 

20.  What  is  the  cost  of  heating  the  water  (exercise  18)  at  the  rate  at 
which  gas  is  sold  in  your  town? 

EXERCISES  AND  PROBLEMS  FOR  REVIEW 

1.  Give  the  equivalent  F.  readings  for  the  following:     (a)   70°  C.; 
(b)  50°  C.;    (c)  25°  C.;    (d)  -  5°  C.;    (e)'  -  25°  C. 

2.  Give  the  equivalent  C.  readings  for  the  following:    (a)  113°  F.; 
(b)  77°  F.;    (c)  14°  F.;    (d)  -  13°  F. 

3.  Find  the  boiling  point  and  the  freezing  point  of  mercury  (a)  on  the 
C.  scale;    (b)  F.  scale. 

4.  Find  the  boiling  point  and  the  freezing  point  of  alcohol  on  (a)  the 
C.  scale;    (b)  F.  scale. 

5.  The  lowest  temperature  thus  far  obtained  is  said  to  be  —  271.3°  C. 
What  is  this  value  on  the  Absolute  scale? 

6.  How  many  calories  of  heat  will  be  required  to  change  the  tem- 
perature of  100  grams  of  the  following  substances  from  0°  C.  to  100°  C.: 
(a)  Water?    (b)  iron?    (c)  lead? 


170  HIGH  SCHOOL  PHYSICS 

7.  100  grams  of  mercury  at  100°  C.  are  stirred  with  100  grams  of  water 
at  20°  C.  and  the  resulting  temperature  is  22.6°  C.     Find  the  specific  heat 
of  the  mercury. 

8.  500  grams  of  copper,  specific  heat  0.09,  temperature  120°  C.,  are 
dropped  into  500  grams  of  water  at  20°  C.     What  is  the  resulting  tem- 
perature? 

9.  A  brass  rod  at  0°  C.  has  a  length  of  200  cm.;   at  100°  C.  its  length 
is  200.36  cm.     Find  its  coefficient  of  expansion. 

10.  The  coefficient  of  expansion  of  nickel  steel  is  0.00001.     A  rod  of 
this  material  having  a.  length  of  5  meters  at  20°  C.  will  have  what  length 
in  centimeters  at  12°  C.? 

11.  What  is  the  coefficient  of  expansion  of  gases,  and  wherein  does  it 
differ  from  the  coefficient  of  expansion  of  solids? 

12.  A  given  mass  of  gas  has  a  volume  of  273  cc.  at  0°  C.     Find  its 
volume  at  (a)  4~  10°  C.;   (b)  —  10°  C.,  the  pressure  remaining  constant. 

13.  State  Gay-Lussac's  law,  and  explain  each  term  in  the  equation: 
v  :  v'  =  T  :  Tf. 

14.  A  given  mass  of  gas  free  to  expand  has  a  volume  of  500  cc.  at 
—  13°  C.     What  will  be  its  volume  at  +  27°  C.,  the  pressure  remaining 
constant? 

15.  A  liter  of  gas  at  —  3°  C.  expands  under  constant  pressure,  due  to  a 
change  of  temperature,  to  1200  cc.     Find  the  change  in  temperature  in 
Centigrade  degrees. 

16.  State  the  laws  of  fusion,  and  illustrate  their  application  to  the 
melting  of  ice. 

17.  Define  heat  of  fusion,  and  explain  what  is  meant  by  saying  that 
the  heat  of  fusion  of  ice  is  80  calories. 

18.  How  many  calories  of  heat  will  be  required  to  change  10  grams  of 
ice  at  zero  to  water  at  20°  C.? 

19.  How  many  calories  of  heat  will  be  required  to  change  10  grams  of 
ice  at  —  10°  C.  to  water  at  the  boiling  point,  the  specific  heat  of  ice  being 
0.5? 

20.  State  two  ways  by  which  the  boiling  point  of  water  may  be  raised. 

21.  To  what  elevation  in  feet  must  water  be  taken  above  sea  level  in 
order  that  its  boiling  point  be  lowered  to  90°  C.? 

22.  State  the  laws  of  boiling,  and  explain  their  application  to  the 
boiling  of  water. 

23.  State  and  illustrate  the  laws  of  evaporation. 

24.  Define  heat  of  vaporization,  and  explain  what  is  meant  by  saying 
that  the  heat  of  vaporization  of  water  is  538  calories. 

25.  How  much  heat  is  required  to  change  100  grams  of  ice  at  0°  C.  to 
100  grams  of  steam  at  100°  C.? 


HEAT  171 

26.  One  kilogram  of  steam  in  a  radiator  at  100°  C.  condenses  to  water 
the  temperature  of  which  falls  to  90°  C.     How  many  calories  of  heat  are 
given  out? 

27.  Give  three  methods  of  producing  cold  by  artificial  means,  and 
give  an  example  illustrating  each. 

28.  Define  and  give  illustrations  of  (a)  conduction;    (b)  convection; 
(c)  radiation.    Explain  wherein  radiation  differs  from  conduction  and 
convection. 

29.  Define  mechanical  equivalent  of  heat,  and  give  its  value  in  (a) 
metric  units;    (b)  English  units. 

30.  The  temperature  of  10  grams  of  water  is  changed  from  20°  C. 
to  the  boiling  point.     Find  (a)  the  number  of  calories  of  heat  required; 
(b)  the  equivalent  value  in  ergs. 

31.  One  quart  of  water  (2  Ibs.)  was  heated  from  the  freezing  point  to 
132°  F.     (a)  How  many  B.T.U.  were  required  to  effect  this  change  of 
temperature?     (b)  The  heat  consumed  by  the  water  is  equivalent  to  how 
many  foot  pounds? 

32.  One  ton  of  hard  coal  of  average  grade  is  burned,     (a)  How  many 
B.T.U.  of  heat  are  liberated?     (b)  How  many  cu.  ft.  of  illuminating  gas 
would  be  required  to  furnish  the  same  quantity  of  heat? 

33.  Suppose  that  10  tons  of  coal  are  required  to  heat  a  certain  house 
for  a  year,  the  heating  apparatus  being  a  hot  air  furnace,  the  efficiency  of 
which  is  60  per  cent.     Find  (a)  the  total  number  of  B.T.U.  liberated  in 
the  furnace;   (b)  the  number  of  heat  units  delivered  through  the  registers. 

34.  In  one  hour  a  10  horse  power  engine  burns  18  Ibs.  of  coal,     (a) 
How  much  work  in  foot  pounds  is  done  by  the  engine  during  the  hour? 

(b)  The  burning  of  18  Ibs.  of  coal  is  equivalent  to  how  many  B.T.U.? 

(c)  18  Ibs.  of  coal  is  equivalent  to  how  much  energy  in  foot  pounds?     (d) 
What  is  the  efficiency  of  the  engine? 

35.  Consult  the  table  of  heats  of  combustion,  Supplement,  607,  and 
determine  the  number  of  calories  of  heat  liberated  in  the  burning  of  10 
grams  of  (a)  gun  powder,  (b)  wood,  (c)  illuminating  gas,  (d)  anthracite 
coal,  (e)  hydrogen. 

For  additional  Exercises  and  Problems,  see  Supplement. 


ELECTRICITY  AND   MAGNETISM 


CHAPTER  VII 
MAGNETISM   AND    ELECTROSTATICS 

MAGNETISM 

265.  The  Natural  Magnet.  In  many  parts  of  the  earth  there 
is  found  a  kind  of  iron  ore  called  magnetite  (FeaCX)  which  pos- 
sesses the  properties  of  a  magnet;  that  is,  it  attracts  iron,  Fig. 
207,  and  when  suspended  points  in  a  north-south  direction, 
Fig.  208.  A  piece  of  this  ore  is  called  a  natural  magnet,  or 


8 


FIG.  207 


FIG.  208 


lodestone.  Any  substance  which  is  attracted  or  repelled  by  a 
natural  magnet  is  called  a  magnetic  substance.  The  name  mag- 
net is  said  to  come  from  the  fact  that  a  magnetic  substance 
was  first  found  in  Magnesia,  Asia  Minor,  and  that  the  term 
lodestone  (leading  stone)  is  probably  due  to  the  fact  that  it 
was  used  in  early  times  by  navigators  as  a  sort  of  crude 
mariners'  compass. 

266.  Properties  of  the  Magnet.  The  fundamental  property 
of  the  magnet  may  be  demonstrated  by  the  following  experi- 
ments :  (a)  Bring  one  end  of  a  bar  magnet  near  some  pieces  of 
iron,  such  as  small  nails,  tacks,  or  iron  filings.  It  attracts  the 


MAGNETISM   AND   ELECTROSTATICS  173 

iron.  The  filings  leap  to  the  poles  of  the  magnet  and  cling 
tenaciously,  (b)  Roll  the  magnet  in  the  iron  filings;  great 
tufts  cling  to  the  ends,  Fig.  209.  (c)  Now  suspend  a  light 
bar  magnet  (a  magnetized  knitting  needle)  so  as  to  move  freely 
about  an  axis,  Fig.  210.  It  takes  a  north-south  position,  the 
end  pointing  toward  the  north  being  called  the  north-seeking 
pole;  the  end  pointing  to  the  south,  the  south-seeking  pole. 


8 


FIG.  209  FIG.  210 

The  north-seeking  pole  is  usually  marked  N  or  + ;  the  south- 
seeking  pole,  S  or  — . 

A  magnet  is  a  magnetic  substance  which  has  poles. 

267.  How  to  Magnetize  a  Body.     Experiment.     If  a  piece 
of  steel,  such  as  a  bit  of  clock  spring,  a  needle,  or  the  blade  of 
a  pocket  knife,  be  drawn  several  times  in  one  direction  across 
the  end  of  a  magnet,  it  will  itself  become  a  magnet.     Consider, 
for  example,  the  case  of  the  knife.     If  the  blade  be  drawn 
across  the  N-pole  of  the  magnet  from  heel  to  point,  the  heel  of 
the  blade  will  be  an  N-pole  and  the  point  an  S-pole,  Fig.  211. 
If  the  blade  be  drawn  in  a  sim- 

_— . 7 \ — 

ilar  manner  across  the  S-pole  of 

the  magnet,  the  polarity  of  the 

blade    will    be    reversed.      The  FlG  2n 

greater  the  number  of  times  the 

steel  is  drawn  across  the  magnet,  the  greater  will  be  the  pole 

strength,  up  to  a  certain  point  at  which  the  steel  is  said  to 

become  magnetically  saturated. 

268.  Magnetic  Substances.     Experiment.     If  the  pole  of  a 
magnet  be  brought  successively  in  contact  with  pieces  of  iron, 
copper,  brass,  wood,  and  paper  it  will  be  found  that  the  iron  is 
strongly  attracted,  while  the  copper,  brass,  wood,  and  paper 


174 


HIGH  SCHOOL  PHYSICS 


are  not  noticeably  affected.  The  iron  is  magnetic;  the  others 
are  non-magnetic.  A  magnetic  substance  is  one  that  is 
attracted  or  repelled  by  a  magnet.  Iron  is  highly  magnetic; 
cobalt  and  nickel  are  also  magnetic,  but  to  a  less  degree  than 
iron.  Some  magnetic  substances;  antimony  (Sb)  and  bismuth 
(Bi)  for  instance,  are  slightly  repelled  by  a  magnet  and  are  said 
to  be  diamagnetic. 

269.  Kinds  of  Magnets.  Magnets  may  be  classified  in 
various  ways,  as  for  example:  (a)  natural  and  artificial  magnets; 
(b)  permanent  and  temporary  magnets;  and  with  reference 
to  their  form;  (c)  bar  and  horseshoe  magnets,  Fig.  212.  All 


FIG.  212 


manufactured  magnets  are  artificial  magnets.  Permanent 
magnets  are  made  of  highly  tempered  steel  and  retain  their 
magnetic  properties  for  a  long  time ;  magnets  made  of  soft  iron 
soon  lose  their  magnetic  properties,  and  for  this  reason  are 
called  temporary  magnets.  Whether  the  magnet 
be  of  the  bar  or  horseshoe  form  is  determined  by 
its  use.  When  we  desire  to  use  a  single  pole,  the 
bar  magnet  is  the  more  convenient;  when,  on  the 
other  hand,  the  maximum  lifting  effect  is  desired, 
the  horseshoe  type  is  employed.  Sometimes  a  short 
piece  of  soft  iron,  called  an  armature  or  keeper,  is 
placed  across  the  end  of  the  magnet,  Fig.  213.  The  use  of 
the  keeper  is  to  prevent  the  magnet  from  losing  its  strength, 
as  will  be  explained  later. 

270.  Law  of  Attraction  and  Repulsion.  Experiment.  Pre- 
sent to  the  north-seeking  pole  of  the  magnetic  needle  the  N-pole 
of  a  magnet,  Fig.  214;  the  like  poles  repel.  Now  present  to  the 
north-seeking  pole  of  the  needle  the  S-pole  of  the  magnet; 


FIG.  213 


MAGNETISM   AND  ELECTROSTATICS 


175 


the  unlike  poles  attract.  From  this  experiment  we  may  deduce 
the  first  law  of  magnets;  namely,  like  poles  repel;  unlike  poles 
attract. 


FIG.  214 


271.  Magnetic  Field  and  Lines  of  Induction.  The  magnetic 
field  is  that  portion  of  space  surrounding  a  magnet  which  is 
affected  by  the  magnet.  Experiment.  The  magnetic  field 


FIG.  215 

may  be  mapped  out  by  sprinkling  fine  iron  filings  upon 
a  glass  plate  and  placing  the  plate  over  a  magnet.  Tap  the 
plate  gently.  The  filings  arrange  themselves  in  curved  lines, 
in  response  to  the  magnetic  force  acting  upon  them,  Fig.  215. 
These  lines  were  called  by  Faraday  lines  of  force,  but  since 
the  tendency  in  modern  practice  is  to  use  the  term  lines  of 
induction,  we  shall  throughout  this  text  speak  of  the  lines  in 
the  magnet  field  as  lines  of  induction.  These  lines  of  induction 
are  conceived  of  as  coming  out  of  the  N-pole  and  passing  in  closed 


176 


HIGH   SCHOOL   PHYSICS 


curves  around  to  the  S-pole,  and  thence  through  the  magnet  back  to 
the  N-pole,  as  shown  in  Fig.  216. 


FIG.  216 


Fia.  217 


FIG.  218 


272.  Effect  of  the  Field  on  a  Magnetic  Needle.  The  posi- 
tion which  a  magnetic  needle  assumes  is  determined  by  the 
direction  of  the  lines  of  induction  of  the  magnetic  field.  If  a 
needle  be  placed  in  a  magnetic  field  as  shown  in  Fig.  217  it  will 
tend  to  set  itself  in  the  direction  of  the  magnetic  force  in  such  a 
manner  that  the  lines  of  induction  enter  the  S-pole  and  come 
out  of  the  N-pole,  Fig.  218. 


•V.'.':;-:.''.?/:.-..'-/*- 


FIG.  219 


273.  Magnetic  Field  for  Like  and  Unlike  Poles,  (a)  Fig. 
219  shows  the  condition  of  the  lines  of  induction  in  a  mag- 
netic field  between  like  poles.  The  crowding  together  of  the 
lines  which  emanate  from  the  N-pole  suggests  an  explanation 
for  the  fact  that  like  poles  repel,  (b)  The  field  between  unlike 
poles  is  shown  in  Fig.  220.  In  this  case  the  curved  lines  tend 
to  contract,  thus  producing  attraction. 


MAGNETISM   AND   ELECTROSTATICS 


177 


274.  Magnetic  Induction.  Experiment.  We  have  seen  that 
when  a  piece  of  iron  is  placed  in  contact  with  a  magnet  it  too 
becomes  magnetized.  The  iron  may  be  magnetized,  however, 


FIG.  220 

without  actually  coming  in  contact  with  the  magnet.  Place 
one  end  of  a  soft  iron  nail  in  iron  filings,  then  bring  near  to  the 
other  end  the  pole  of  a  bar  magnet.  If  now  both  nail  and  mag- 
net be  lifted  it  will  be  observed  that  tufts  of  iron 
filings  cling  to  the  lower  end  of  the  nail,  Fig.  221, 
thus  showing  that  it  is  magnetized  even  though  not 
in  actual  contact  with  the  permanent  magnet.  When 
the  magnet  is  removed,  then  the  nail  at  once  loses 
its  magnetism,  the  iron  filings  falling  away.  While 
the  nail  is  influenced  by  the  presence  of  the  magnet, 
it  is  said  to  be  magnetized  by  induction.  If  the 
pole  of  a  magnet  be  brought  near  a  piece  of  iron 
or  other  magnetic  substance,  there  will  be  induced 
in  the  iron  on  the  side  next  the  magnet  a  pole  of 
the  opposite  kind,  and  in  the  side  farthest  from  the 
magnet  a  pole  of  the  same  kind. 

275.  Magnetic  Transparency.  A  great  many  substances 
such  as  glass,  paper,  wood,  etc.,  seem  to  be  transparent  to 
magnetic  induction.  Such  substances  are  said  to  be  "  magnet- 
ically transparent."  Experiment.  If  icon  filings  be  sprinkled 
on  a  glass  plate  and  the  plate  be  placed  upon  a  magnet,  the 


FIG.  221 


178 


HIGH  SCHOOL  PHYSICS 


FIG.  222 


filings  will  become  strongly  magnetized,  thus  showing  that 
the  glass  is  magnetically  transparent.  If  we  place  between  a 
magnetic  pole  and  a  piece  of  iron  a  sheet  of  paper,  Fig.  222, 
the  iron  will  be  attracted  to  the  magnet,  show- 
ing that  the  paper  is  magnetically  transparent. 

276.  Magnetic  Shields.  We  have  learned  that 
glass  is  magnetically  transparent.  Iron  on  the 
other  hand  is  not  magnetically  transparent  in  the 
sense  in  which  glass  is.  This  fact,  together  with 
the  magnetic  shielding  effect  of  iron,  is  very  well 
shown  in  Figs.  223,  224.  In  Fig.  223  there  is  shown 
the  passage  of  the  lines  of  induction  through  the 
sides  of  a  glass  vessel  placed  in  a  strong  magnetic 
field.  Fig.  224  illustrates  the  shielding  effect  of 
an  iron  ring,  the  lines  of  induction  passing  around  through 
the  iron  from  one  pole  to 
the  other.  An  object,  a 
watch  for  example,  placed 
at  A  within  the  ring  will 
be  effectually  shielded  from 
the  magnetizing  force  of 
the  field. 

277.  The  Effect  of  Break- 
ing a  Magnet.     Experiment.     Suppose  that  we  magnetize  a 
thin  strip  of  steel  (a  piece  of  clock  spring).     It  has  a  pole  at 

each  end  and  a  neutral 
point  in  the  middle. 
Now  if  this  magnet  be 
broken  at  the  middle  it 
will  be  found  that  each 
piece  is  a  magnet,  Fig. 
225.  If  each  piece  be 
again  broken  the  smaller 
pieces  will  still  be  magnets.  Thus  we  may  conceive  the  break- 
ing process  to  go  on  until  the  molecule  is  reached.  The  con- 


FIG.  223 


FIG.  224 


MAGNETISM   AND  ELECTROSTATICS  179 

elusion  from  this  and  other  experiments  is  that  a  magnet 
possesses  its  magnetic  properties  because  of  the  fact  that  its 
molecules  are  magnets. 


JS 


FIG.  225 

278.  The  Molecular  Condition  of  Unmagnetized  and  Mag- 
netized Iron.  When  a  bar  of  iron  is  unmagnetized  its  mole- 
cules are  supposed  to  point  in  every  conceivable  direction,  as 
shown  in  Fig.  226.  When  it  is  magnetized  the  molecules  point 
in  a  definite  direction,  Fig.  227,  thus  giving  the  bar  polarity. 


!^C-7^0i 


FIG.  226  FIG.  227 

If  a  bar  magnet  be  dropped  or  jarred  violently,  it  is  said  to  lose 
its  magnetism.  What  really  happens  is  that  the  molecules 
rearrange  themselves  again,  taking  up  the  position  as  in  Fig. 
226.  Strictly  speaking,  the  bar  has  as  much  magnetism  as 
before;  what  it  has  lost  is  its  polarity. 

279.  Consequent  Poles.  Experiment.  Every  magnet  has 
two  poles.  A  bar  may  be  magnetized,  however,  so  that  it  will 
have  within  itself  a  number  of  magnets,  and  hence  a  number 


FIG.  228 

of  poles.  The  poles  which  occur  in  a  magnet  other  than  at 
the  ends  are  called  consequent  poles.  If  the  poles  of  a  perma- 
nent magnet  be  drawn  along  a  piece  of  steel  (knitting  needle), 
skipping  at  several  points,  Fig.  228,  the  needle  will  contain 


180  HIGH  SCHOOL  PHYSICS 

two  or  more  consequent  poles.  It  is  possible  to  magnetize  a 
steel  bar  in  such  a  way  that  both  ends  may  be  either  N-poles 
or  S-poles.  The  bar  will  of  course  in  this  case  contain  conse- 
quent poles  opposite  in  sign  to  those  at  the  end. 

280.  The  Earth  a  Magnet.  Experiment.  Suspend  above  a 
long  bar  magnet  NS,  Fig.  229,  a  short  magnetic  needle  ns. 
When  the  needle  is  at  the  neutral  point,  its  position  is  hori- 
zontal; when  it  is  carried  from  this  point  toward  either  pole, 


N 


FIG.  229 

it  dips  more  and  more,  until  the  pole  is  reached,  when  its  posi- 
tion is  vertical.  Now  if  a  magnetic  or  dipping  needle  be  car- 
ried on  the  surface  of  the  earth  from  the  equator  toward  the 
poles,  it  will  be  observed  to  dip  in  a  similar  manner.  This 
means  that  the  earth  behaves  exactly  as  if  it  were  a  magnet, 
having  one  magnetic  pole  near  the  north  geographic  pole 
and  the  other  near  the  south  geographic  pole.  The  earth's 
magnetic  pole  at  the  north  corresponds  to  the  S-pole  of  a 
bar  magnet;  the  magnetic  pole  at  the  south  corresponds  to 
the  N-pole  of  a  bar  magnet.  Since  unlike  poles  attract,  we 
thus  understand  why  the  N-pole  of  a  magnetic  needle  points 
toward  the  north. 

The  magnetic  poles  of  the  earth  do  not  coincide  with  the  geo- 
graphic poles,  the  magnetic  pole  of  the  north,  for  example, 
being  more  than  1000  miles  from  the  geographic  pole.  The 
magnetic  pole  of  the  north  is  in  the  northern  part  of  Brit- 
ish America,  about  70°  N.  latitude  and  longitude  97°  W., 
Fig.  230. 


MAGNETISM   AND   ELECTROSTATICS 


181 


281.  The  Angle  of  Declination.     We  sometimes  say  that  the 
magnetic  needle  points  north-south.     This,  however,  is  very 
rarely  true.     True  north  from  any  point  on  the  earth  is  the  direc- 
tion from  that  point  to  the  north  geographic  pole.     Now  the  mag- 
netic needle  points  to  the  magnetic  pole,  and  as  we  have  already 
learned,  these  two  poles  do  not 

coincide.     The  angle  made  by 

the  needle  and  true  north  is 

called  the  angle  of  declination. 

Experiment.     To  find  the  angle 

of  declination  for  a  given  place 

one   may   proceed   as  follows: 

Drive    two    stakes    into    the 

ground  in  such  a  position  that 

a  string  stretched  from  one  to 

the    other   will    point    to    the 

North   star,  which   determines 

very   closely  the    direction   of 

the     north     geographic     pole. 

The  string  therefore  lies  on  a  geographic  meridian;  that  is, 

it  points  true  north-south.     Now  place  a  long  magnetic  needle 

just  below  the  string.     The  angle  made  by  the  needle  and 

the  string  is  the  angle  of  declination.     The  declination  for 

Ann  Arbor,  Mich.,  is   at    present  very  nearly  two  degrees, 

the  needle  pointing  west  of  true  north. 

In  some  places  the  needle  points  to  true  north.  A  line 
drawn  through  such  places  is  called  a  line  of  no  declination,  or 
an  agonic  line.  At  present  the  line  of  no  declination  for  the 
United  States  passes  near  Lansing,  Mich.,  Fort  Wayne,  Ind., 
Cincinnati,  Ohio,  and  Charleston,  S.  C.  For  all  points  east 
of  this  line  the  declination  is  toward  the  west;  for  points  west 
of  it,  the  declination  is  toward  the  east. 

282.  Variation  in  the  Direction   of   the   Magnetic   Needle. 
The  magnetic  poles  are  not  fixed  in  position.     The  north  mag- 
netic pole,  for  example,  swings  slowly  back  and  forth  in  an 


FIG.  230.       Magnetic   Pole  of 
Northern  Hemisphere 


182  HIGH  SCHOOL  PHYSICS 

east-west  direction,  requiring  several  centuries  to  make  a  com- 
plete vibration.  This  shifting  of  the  magnetic  poles,  together 
with  other  causes  not  very  well  understood,  gives  rise  to  a 
continual  variation  in  the  angle  of  declination.  In  surveying 
land  it  is  very  important  that  this  variation  shall  be  known. 
A  systematic  record,  therefore,  of  all  variations  of  terres- 
trial magnetism  are  made  and  kept  by  the  United  States 
government. 

STATIC  ELECTRICITY 

283.  The  Nature  of  Electricity.  Phenomena  connected  with 
electrical  discharges,  as  seen  in  the*  flash  of  lightning,  have  always 
been  a  part  of  man's  experience,  and  in  modern  times  the  use  of 
electricity  in  the  production  of  light,  the  ringing  of  door  bells, 
and  the  running  of  trolley  cars  has  become  so  familiar  as  to 
excite  no  more  wonder  than  the  phenomena  associated  with 
gravitation,  heat,  or  sound.  There  is,  however,  one  very  im- 
portant difference  between  these  two  sets  of  phenomena.  In 
the  case  of  heat,  for  example,  we  know  not  only  what  it  does 
but  what  it  is;  in  the  case  of  electricity,  on  the  other  hand,  we 
know  what  it  does,  but  we  do  not  know  what  it  is.  We  know 
that  the  energy  of  a  current  of  electricity  may  be  transformed 

into  heat,  light,  or  mechanical 
motion,  but  what  electricity  itself 
is  no  one  at  present  knows. 

284.  Electrification.  Experi- 
ment. Since  the  days  of  the  an- 
cient Greeks  it  has  been  known 
that  when  certain  bodies  were 
rubbed  together  they  possessed 
the  power  of  attracting  other 
FlG  23i  bodies.  For  example,  if  a  glass 

rod  be  rubbed  with  silk  it  will 

attract  a  light  pith  ball  or  bits  of  paper,  Fig.  231.  We  say 
that  the  glass  rod  is  electrified.  In  a  like  manner  we  may 


MAGNETISM   AND  ELECTROSTATICS  183 

electrify  a  stick  of  sealing  wax  by  rubbing  it  with  flannel  or 
cat's  fur.  Other  familiar  illustrations  are  seen  in  the  electri- 
fication of  a  rubber  comb  when  drawn  through  the  hair,  or  in 
the  electric  discharge  which  occurs  when  the  hand  is  drawn 
over  a  cat's  back  on  a  dry  day. 

A  study  of  the  phenomena  of  electrification  is  usually  consid- 
ered under  that  division  of  electricity  known  as  static  electricity. 
Electricity  in  a  state  of  rest  is  called  static  electricity ;  electricity 
in  motion,  current  electricity. 

285.  Two  Kinds  of  Electrification.     It  was  early  discovered 
that  there  are  two  kinds  of  electrification,  one  called  positive 
(+),  the  other  negative  (  — ).     A  glass  rod  rubbed  with  silk  is 
said  to  be  positively  electrified;   a  stick  of  sealing  wax  rubbed 
with  flannel  or  cat's  fur,  negatively  electrified.    There  are  many 
other  substances  which  may  be  electrified,  some  positively  and 
some  negatively.    We  shall,  however,  for  the  sake  of  simplicity 
and  clearness,  think  of  glass  rubbed  with  silk  as  a  type  of  posi- 
tively electrified  bodies,  and  sealing  wax  rubbed  with  flannel  as 
a  type  of  negatively  electrified  bodies.     We  shall  also  speak 
of  electrified  bodies  as  being  charged  positively  or  negatively, 
as  the  case  may  be. 

There  is  no  very  good  reason  for  calling  the  electrical  charge 
on  glass  positive  (+)  and  that  on  sealing  wax  negative  (  — ), 
other  than  the  fact  that  these  terms  were  adopted  when  the 
subject  was  first  studied.  (Supplement,  597.) 

286.  Attraction  and  Repulsion.    -Among  the  most  familiar 
phenomena  of  electrification  are  those  of  attraction  and  repul- 
sion.    If  a  rod  be  electrified  and  brought  near  a  light  body, 
such  as  a  pith  ball,  two  things  may  be  observed:   (a)  The 
pith  ball  is  at  first  attracted  to  the  electrified  rod,  Fig.  232, 
and  (b)  after  a  moment  in  contact,  it  is  repelled. 

It  is  important  to  note  that  whenever  an  electrified  body  is  brought 
near  another  body,  attraction  or  repulsion  always  results. 

287.  Laws     of     Attraction     and     Repulsion.     Experiment. 
Charge  a  glass  rod  positively  and  suspend  it  in  a  stirrup,  as 


184 


HIGH   SCHOOL   PHYSICS 


shown  in  Fig.  233.     Bring  near  the  suspended  rod  another 
glass  rod  also  positively  charged.     The  two  repel  each  other. 


FIG.  232 


Now  present  to  the  suspended  glass  rod  a  stick  of  sealing  wax 
which  has  been  negatively  charged.   The  two  attract  each  other. 


FIG.  233 

Law  of  signs:  Charges  of  like  sign  repel;  charges  of  unlike 
sign  attract. 

288.  Discussion  of  Attraction  and  Repulsion.  We  are  now 
prepared  to  explain,  in  a  measure,  the  phenomena  of  attraction 
and  repulsion.  If  a  glass  rod  positively  charged  be  brought  near 
a  pith  ball,  Fig.  234,  there  will  be  induced  on  the  side  of  the  pith 
ball  nearest  the  rod  a  —  charge,  and  on  the  side  farthest  from 
the  rod  a  +  charge.  The  positive  charge  on  the  ball  is  exactly 
equal  in  quantity  to  the  negative  charge.  Now  since  unlike 
signs  attract  and  like  signs  repel,  it  follows  that  the  —  charge 
will  tend  to  move  toward  the  glass  rod  and  the  +  charge  away. 


MAGNETISM   AND  ELECTROSTATICS 


185 


FIG.  234 


The  force  of  attraction,  however,  is  greater  than  the  force  of 

repulsion,  since  the  —  charge  on  the  ball  is  nearer  to  the  rod 

than  is  the  -f  charge.     The  moment  the  two 

come  in  contact,  the  negative  charge  on  the 

ball  is  neutralized  by  some  of  the  positive 

charge  on  the  rod,  and  there  remains  on  both 

rod  and  ball  positive  charges.     Since  charges 

having  like  signs  repel  each  other,  the  ball 

is  now  driven  away  from  the  rod. 

The  above  explanation  of  attraction  and  repulsion  will  apply 
whether  the  charging  body  has  either  a  negative  or  a  positive 
charge  upon  it. 

289.  The  Two  Kinds  of  Electrification  Equal  in  Quantity. 
Experiments  seem  to  prove  that  whenever  a  body  is  charged 
with  electrification  of  one  kind  there  is  somewhere  developed 
an  equal  charge  of  the  opposite  sign.  Thus  when  a  glass  rod 
is  rubbed  with  silk,  a  positive  charge  is  developed  upon  the 
rod  and  an  equal  negative  charge  is  developed  upon  the  silk; 
similarly  when  sealing  wax  is  rubbed  with  flannel,  a  negative 
charge  occurs  on  the  sealing  wax  and  an  equal  positive  charge 
upon  the  flannel. 

To  prove  that  positive  and  negative  charges  are  always  devel- 
oped in  equal  amounts,  Faraday  used  an  ebonite  rod  upon 
which  was  fitted  a  flannel  cap,  Fig.  235.  He  electri- 
fied the  two  bodies  by  twisting  the  rod  inside  the  cap 
and  then  removed  the  latter  by  means  of  a  silk  string 
attached  to  it.  He  tested  both  the  charge  upon  the 
rod  and  that  upon  the  cap  and  found  that  not  only 
was  the  charge  on  the  rod  positive  and  that  on  the 
cap  negative,  but  also  that  the  two  were  exactly 
equal  in  quantity. 

290.  Charging  by  Conduction  and  Induction.  A 
body  may  be  charged  electrically  in  two  ways:  by  conduc- 
tion and  by  induction. 

(a)  If  a  charged  body  be  brought  in  contact  with  another 


FIG.  235 


186 


HIGH   SCHOOL   PHYSICS 


body,  some  of  the  electricity  on  the  first  will  flow  off  upon  the 
second  body.  Thus  the  second  body  is  said  to  be  charged  by 
conduction. 

(b)  If,  on  the  other  hand,  the  charged  body  be  brought  near 
a  second  body,  there  will  occur  upon  the  latter  two  charges 

equal    in   quantity   and   opposite   in 
>\    sign,  Fig.    236.     In  this  case  the  + 
~)   charge  is   said   to  be  bound ;  the  - 
charge  is  free,  and   tends  to  get  as 
far    as    possible   from    the  —  charge 
FIG.  236  on  the   rod.     If  a  finger  be  touched 

to  the  charged  body  B,  the  free  —  charge  will 
flow  off.  If  now  the  charging  rod  A  be  re- 
moved, there  will  remain  on  B  the  +  charge. 
B  is  then  said  to  be  charged  by  induction. 

291.  The  Electroscope.  An  electroscope  is  an 
instrument  for  detecting  the  presence  of  charges 
Of  static  electricity.  It  consists  of  two  leaves  of 
gold  foil  attached  to  a  metal  rod,  Fig.  237,  the 
whole  being  enclosed  in  a  glass  flask.  The  ob- 
ject of  the  flask  is  to  protect 
the  leaves  of  the  electroscope 
from  drafts  of  air  or  injuries  from  contact. 
292.  How  to  Charge  the  Electroscope  by 
Conduction.  Experiment.  If  a  charged  body 
be  brought  in  contact  with  the  electroscope, 
Fig.  238,  some  of  the  electricity  will  flow  off 
the  body  onto  the  electroscope,  distributing 
itself  over  the  knob  and  leaves.  The  leaves 
of  the  instrument,  being  charged  with  elec- 
tricity of  like  signs,  will  repel  each  other. 
When  the  charging  body  is  removed  it  will  have  lost  a  quan- 
tity of  electricity  equal  to  that  gained  by  the  electroscope. 
When  an  electroscope  is  charged  by  conduction  the  charge  upon 
it  is  similar  in  sign  to  that  on  the  charging  body. 


FIG.  237 


FIG.  238 


MAGNETISM   AND  ELECTROSTATICS 


187 


FIG.  239 


Sometimes  it  is  desired  to  convey  a  definite  portion  of  a 
charge  to  the  electroscope.  This  may  be  done  by  means  of  a 
proof  plane,  which  consists  of  a  small  metal  disc  attached  to 
a  nonconducting  handle,  Fig.  239,  and  which 
is  used  to  transfer  small  charges  from  one 
body  to  another.  For  example,  if  a  proof 
plane  be  touched  to  a  charged  body,  such  as 
the  pole  of  an  electric  machine,  and  then 
conveyed  to  the  knob  of  the  electroscope,  a 
slight  divergence  of  the  leaves  will  result. 
Upon  conveying  a  second  charge  a  further  divergence  will 
occur.  In  this  way  it  is  possible  to  convey  as  much  elec- 
tricity to  the  electroscope  as  is  desired. 

293.  How  to  Charge  an  Electroscope  by  Induction.  Experi- 
ment. Bring  a  charged  body  (positively  charged,  say)  near 
the  knob  of  the  electroscope.  There  will  be  induced  upon  the 
knob  a  negative  charge  and  upon  the  leaves  an  equal  positive 
charge.  The  negative  charge  is  bound,  and  the  positive  charge 
free.  Now  if  a  ringer  be  touched  to  the  electroscope,  the  free 
positive  charge,  being  repelled  by  the  charge  on  the  glass  rod, 
will  flow  off  to  the  earth.  Remove  the  finger,  and  afterward 
remove  the  charging  body.  There  will  then  remain  upon  the 
electroscope  a  negative  charge  which  will  distribute  itself  over 
the  metallic  part  of  the  instrument.  The  electroscope  is  now 
charged  by  induction,  Fig.  240.  It  will  be  noted  that  when  the 


FIG.  240 


188 


HIGH   SCHOOL  PHYSICS 


FIG.  241 
Electrophorus 


electroscope  is  charged  in  this  manner,  that  is,  by  induction, 
the  charge  upon  it  is  of  the  opposite  sign  to  that  on  the  charging 
body. 

294.  The  Electrophorus.     It  is  sometimes  desirable  to  charge 
a  body  with  a  larger  quantity  than  can  be  obtained  upon  a 

glass  rod  or  a  stick  of  sealing  wax.  To 
do  this  an  electrophorus  may  be  em- 
ployed, Fig.  241.  This  consists  of  a 
shallow  dish  containing  resin,  sealing 
wax,  vulcanite,  or  some  similar  non- 
conducting material.  A  metal  disc  of 
a  size  suitable  to  fit  the  dish  is  provided 
with  an  insulating  handle. 

To  charge  the  electrophorus  appara- 
tus, we  rub  the  nonconducting  material 
with  flannel  or  cat's  fur,  thus  giving  it  a 
—  charge,  Fig.  242.  If  now  we  place  the  metal  disc  upon  the 
surface  of  the  apparatus,  only  a  very  small  quantity  of  elec- 
tricity will  flow  to  the 
metal,  because  of  the 
nonconducting  prop- 
erty of  the  resin  or 
other  substance  used. 
The  —  charge  on  the 
resin  induces  a  + 
charge  on  the  under  side  of  the  disc  and  an  equal  —  charge 
on  the  upper  side.  In  this  case  the  -f  charge  on  the  disc  is 
bound,  the  —  charge  is  free.  Now  if  the  finger  be  touched  to 
the  disc,  the  free  —  charge  will  flow  to  the  earth,  leaving  be- 
hind the  bound  +  charge.  The  disc  may  be  removed  and 
the  charge  on  its  surface  conveyed  to  any  other  body. 

295.  The  Electric  Machine.     An  electric  machine,  Fig.  243, 
is  nothing  more  than  a  device  involving  the  principle  of  the 
electrophorus.     It  consists  usually  of  one  or  more  glass  plates, 
which  on  being  rotated  become  charged,  mainly  by  induction. 


FIG.  242 


MAGNETISM   AND  ELECTROSTATICS 


189 


A  cross  metal  bar  serves  to  draw  off  the  free  electricity  from  the 
rotating  disc,  and  the  bound  charge  is  then  transferred  to  the 
discharging  points. 

For  description  of  Toepler-Holtz  and  Wimshurst   electric 
machines,  see  Supplement,  569  and  570. 


FIG.  243 


FIG.  244 


296.  The  Leyden  Jar.  The  Leyden  jar  consists  of  a  glass 
vessel  coated  about  two-thirds  the  way  up  on  both  the  inside 
and  the  outside  with  tin  foil,  Fig.  244.  A  metal  conductor  com- 
municates with  the  inner  coating  of  the  vessel.  To  charge  the 
jar  we  grasp  the  outer  coating  in  the  hand  and  place  the  knob 
in  contact  with  one  of  the  poles  of  an  electric  machine,  thus 
charging  the  inner  coating  by  conduction.  The  outer  coating 
becomes  charged  through  the  glass  by  induction.  Suppose, 
for  example,  that  the  inner  coating  of  the  jar  have  a  +  charge, 
Fig.  245.  Then  the  bound  charge  on  the  outside  will  be  nega- 
tive and  the  free  -f-  charge  will  flow  off  from  the  hand  to  the 
earth. 

To  discharge  the  jar  a  conductor  having  a  glass  handle  is 
used,  Fig.  246.  Sometimes  it  is  possible  to  obtain  two  or  more 
sparks  from  the  jar.  This  is  due  to  what  is  called  the  residual 
charges.  The  glass  when  charged  is  supposed  to  be  under  a 
state  of  strain  and  does  not  entirely  relieve  itself  on  the  first 
discharge. 


190 


HIGH   SCHOOL  PHYSICS 


The  Ley  den  jar  acts  as  a  condenser.  An  electrical  condenser 
is  a  device  for  increasing  the  charge  on  a  conductor  without  in- 
creasing the  potential  (Art.  298).  It  consists  of  two  or  more 
sheets  of  tin  foil  separated  by  glass,  paraffin  paper,  or  other 

O 


FIG.  245 


FIG.  246 


nonconducting  medium,  called  a  dielectric.  Condensers  are 
very  largely  used  in  induction  coils  (Art.  398),  and  in  many 
other  kinds  of  modern  electrical  apparatus  such  as  the  tele- 
phone and  wireless  telegraph. 

297.   The  Charge  on  the  Glass.     By  means  of  a  dissected 
Ley  den  jar,  Fig.  247,  it  is  possible  to  prove  that  the  charge 


FIG.  247 


resides  on  the  glass  and  not  upon  the  metal  conductor  (tin  foil). 
Let  the  jar  be  charged.  Then  by  means  of  a  glass  rod  lift  the 
inner  coating  out  and  remove  the  glass  jar.  Now  bring  the 


MAGNETISM   AND   ELECTROSTATICS 


191 


two  metal  coatings  together.  No  spark  is  produced,  showing 
that  there  is  no  charge  upon  them.  Now  put  the  parts  of  the 
jar  together  again,  using  the  glass  rod  to  handle  the  inner  coat- 
ing as  before,  and  connect  the  outer  coating  with  the  knob  by 
means  of  the  discharging  apparatus.  A  bright  spark  will  be 
obtained,  thus  showing  that  the  charge  was  upon  the  glass  and 
not  upon  the  metal. 

298.  Electric   Pressure   or   Potential.       We  have  thus  far 
been  speaking  of  charged  bodies  in  a  very  general  way.     It  is 
now   important   that   we   get   a 

little  clearer  notion  of  what  is 
meant  by  the  terms  positive 
charge  and  negative  charge,  and 
also  their  relation  to  each  other. 
Let  us  suppose  that  we  have 
four  tanks  partly  filled  with 
water,  Fig.  248,  two  above  the 
surface  of  the  earth  and  two 
below.  The  water  in  each  tank 
exerts  a  pressure.  The  pres- 
sure in  A  is  greater  than  that  in  B]  the  pressure  in  C  greater 
than  that  in  D.  Now  this  pressure  exerted  by  the  water  is  some- 
what analogous  to  the  electrical  pressure  exerted  by  a  charged  body. 
Tanks  A  and  B  may  be  considered  as  analogous  to  positively 
charged  bodies;  tanks  C  and  D  to  negatively  charged  bodies. 
And  just  as  we  consider  the  line  MN  as  the  zero  line  for  the 
water  pressure  in  the  tank,  so  too  for  electricity  we  consider 
the  earth  as  being  of  zero  electric  pressure  or  potential. 

Bodies  charged  positively  have  a  potential  higher  than  that  of 
the  earth;  bodies  charged  negatively  have  a  potential  lower  than 
that  of  the  earth. 

299.  The  Electric  Current.     If  two  bodies  of  different  poten- 
tial (electrical  pressure)  be  connected  by  means  of  a  wire  or 
other  conductor,  a  portion  of  the  charge  on  the  body  of  high 
potential  will  be  conveyed  along  the  conductor  to  the  body  of 


FIG.  248 


192 


HIGH   SCHOOL   PHYSICS 


FIG.  249 


low  potential.  This  transfer  of  electricity  from  one  body  to 
another  gives  rise  to  what  is  called  an  electric  current.  Just 
as  water  may  flow,  in  the  case  of  the  four  tanks  of  Fig.  248, 
from  A  to  B,  or  from  C  to  D,  or  from  either  A 
or  B  to  C  or  D,  a  current  of  electricity,  in  an 
analogous  manner,  may  flow  between  (a)  two 
positively  charged  bodies,  (b)  two  negatively 
charged  bodies,  (c)  or  between  positively  and 
negatively  charged  bodies,  provided  always 
that  one  of  the  bodies  is  at  a  higher  potential 
than  the  other. 

300.  Static  Charges  Reside  upon  the  Sur- 
face. Experiment.  Place  a  tin  cup  or  other 
hollow  metallic  vessel  upon  a  nonconducting 
base  of  glass  or  paraffin  and  charge  the  cup 
from  an  electric  machine,  Fig.  249.  Touch  a 
proof  plane  to  the  outside  of  the  vessel  and 
then  to  the  knob  of  an  electroscope;  the  leaves  are  affected, 
showing  that  there  is  a  charge  on  the  outside  of  the  vessel. 
Now,  touch  the  proof  plane  to  the  inside  of  the  vessel  and 
again  to  the  knob  of  the  electroscope;  the  leaves  are  not 
affected,  showing  that  there  is  no  charge  on  the  inside.  A 
static  charge  resides  on  the  outside  of  a  conductor.  To  prove 
that  even  for  very  high  potentials  the  charge  remains  upon 
the  surface,  Faraday  used  a  cage  made  of  metal  rods,  inside 
of  which  he  placed  a  sensitive  electroscope.  He  then  charged 
the  cage  so  heavily  that  a  spark  discharge  occurred  from 
different,  points  on  the  surface;  the  electroscope,  however,  was 
not  affected  in  the  slightest  degree. 

It  has  been  found  by  many  such  experiments  that  a  charge 
of  electricity  at  rest,  that  is,  static  electricity,  always  resides  upon 
the  surface  of  the  conductor. 

301.  Distribution  of  the  Charge.  The  distribution  of  the 
charge  of  static  electricity  upon  the  surface  of  a  conductor 
depends  upon  two  factors:  (a)  the  shape  of  the  conductor,  (b) 


MAGNETISM   AND  ELECTROSTATICS  193 

the  presence  or  absence  of  other  charged  bodies.  In  the  case 
of  a  spherical  conductor  free  from  the  influences  of  other  bodies, 
the  charge  is  distributed  uniformly  over  the  surface,  Fig.  250.  In 
case  there  are  present  other  charged  bodies  the  charge  is  distrib- 
uted somewhat  as  shown  in  Fig.  251.  In  the  case  of  an  irregular 
shaped  body,  the  charge  has  its  greatest  density  at  the  pointed  por- 
tion of  the  conductor,  Fig.  252. 


FIG.  250  FIG.  251  FIG.  252 

302.  The  Influence  of  Sharp  Points.     The  effect  of  sharp 
points  in  connection  with  conductors  is  of  great  importance  in 
the  operation  of  certain  types  of  electrical  apparatus,  and  also 
in  the  application  of  the  lightning  rod  in  the  protection  of  build- 
ings.     A  sharp  point  serves  to  discharge  the  electricity  upon  a 
body,  as  may  be  shown  by  the  following  experiment.    If  an  elec- 
troscope be  charged  the  leaves  will  remain  apart  for   some 
considerable  time,  depending  upon  the  condition  of  the  atmos- 
phere and  the  nature  of  the  instrument.     (Supplement,  571.) 
If  now  the  head  of  a  pin  or  other  sharp  pointed  body  fastened 
to  the  end  of  a  glass  rod  be  brought  in  contact  with  the  knob 
of  the  electroscope,  the  leaves  will  collapse  very  quickly,  thus 
showing  the  effect  of  the  discharging  point. 

303.  Lightning.     Benjamin  Franklin  was  one  of  the  first  to 
demonstrate  the  similarity  between  that  discharge  of  atmos- 
pheric electricity  known  as  lightning  and  the  discharge  from  a 
Leyden  jar  or  an  electric  machine.      During  a  thunderstorm  he 
sent  up  a  kite  having  a  pointed  wire  at  the  top.     The  kite  was 
provided  with  a  hempen  string,  to  the  lower  end  of  which  was 
attached  a  key,  Fig.  253.     In  order  to  control  the  kite  and  at 
the  same  time  to  prevent  the  charge  from  passing  through  his 
body,  Franklin  fastened  to  the  kite  string  a  piece  of  nonconduct- 


194  HIGH   SCHOOL  PHYSICS 

ing  silk  ribbon,  the  end  of  which  he  held  in  his  hand.  When 
the  hempen  string  became  wet  he  succeeded  in  drawing  from 
the  key  electric  sparks  which  he  concluded  were  similar  in  every 
respect  to  those  that  came  from  the  Leyden  jar. 

Clouds  become  charged  in  a  manner  which  may  be  some- 
what analogous  to  that  of  the  charge  on  the  plates  of  an  elec- 
tric machine.  When  two  clouds  oppositely  charged  come  near 
to  each  other  the  potential  (electric  pressure)  may  become  so 


FIG.  253.  —  Franklin's  Kite  Experiment 

great  that  discharge  takes  place,  resulting  in  a  flash  of  light- 
ning. The  discharge  from  one  cloud  to  another  or  from  a  cloud 
to  the  earth  is  similar  in  every  respect  to  the  discharge  between 
the  knobs  of  an  electric  machine,  except  that  in  the  case  of 
the  atmospheric  discharge  the  phenomenon  occurs  on  a  very 
much  grander  scale. 

Observers  sometimes  imagine  that  they  can  see  the  flash  of 
lightning  go  from  one  cloud  to  another.  This  is,  however,  an 
optical  illusion,  since  the  discharge,  as  in  the  case  of  an  elec- 


MAGNETISM   AND  ELECTROSTATICS 


195 


trie  machine  or  Ley  den  jar,  is  oscillatory;  that  is,  the  discharge 
occurs  back  and  forth  a  great  many  times  in  a  second.  The 
thunder  which  is  associated  with  lightning  is  caused  by  the  ex- 
pansion of  air  created  by  the  flash.  Accompanying  a  lightning 
flash  there  is  a  sudden  increase  in  volume  of  the  air  along  the 
path  of  discharge,  giving  rise  to  violent  vibrations  of  the  atmos- 
phere and  causing  the  crashing  or  rumbling  noise  called  thun- 
der. Thunder,  therefore,  always  follows  the  lightning  flash  and 
never  precedes  it. 


FIG.  254.  — The  Lightning  Rod 

304.  The  Lightning  Rod.  The  lightning  rod  consists  of  a 
metal  conductor  provided  with  one  or  more  sharp  points,  and 
having  the  lower  end  connected  with  the  earth,  Fig.  254.  The 
exact  importance  of  the  lightning  rod  as  a  protection  for  build- 
ings has  not,  up  to  the  present  time,  been  thoroughly  deter- 
mined. It  is  believed,  however,  that  its  principal  functions  are 
to  furnish  (a)  a  means  of  silent  discharge  between  the  earth 


196 


HIGH  SCHOOL  PHYSICS 


and  the  electrified  atmosphere  above,  as  illustrated  by  the 
principle  of  discharging  points,  and  (b)  to  furnish  a  conductor 
to  the  earth  in  case  the  building  is  struck.  It  is  now  known 
that  a  lightning  rod  need  not  be  made  of  any  particular  sort  of 
metal  or  that  it  be  of  any  special  shape;  heavy  iron  wire  serves 
the  purpose  very  well.  The  important  facts  to  be  kept  in  mind 
in  installing  lightning  rods  are  (a)  that  the  wires  are  to  be  so 
put  up  as  to  furnish  a  number  of  discharging  points  at  the  top 
of  the  building,  and  (b)  that  the  lower  end  be  buried  deep 
enough  so  as  to  be  in  contact  with  moist  earth. 

305.  The  Electric  Screen.  It  is  believed  that  the  most 
effective  protection  from  lightning  is  furnished  by  metal  screens. 

This  may  be  demonstrated 
by  a  simple  device  involving 
the  principle  of  Faraday's 
celebrated  screen  experi- 
ment. Within  a  wire  screen 
place  a  small  electroscope 
and  then  put  the  apparatus 
thus  formed  between  the 
knobs  of  an  electric  ma- 

chine,  Fig.  255.     When  the 

FIG.  255.  —  Electric  Screen  machine  is  operated  a  dis- 

charge   takes   place    across 

the  screen,  during  which  the  electroscope  will  remain  un- 
disturbed. 

Warehouses  and  other  buildings  containing  highly  inflam- 
mable material  are  sometimes  protected  in  this  way  by  having 
stretched  over  them  a  network  of  metal  conductors  which  are 
thoroughly  grounded  at  a  number  of  points.  The  screen  effects 
of  the  metal  roofs,  girders,  gas  and  water  pipes  which  cover 
the  modern  structures  of  our  cities  probably  explain  why  such 
buildings  are  so  rarely  injured  by  lightning. 


CHAPTER  VIII 
CURRENT   ELECTRICITY 

THE  ELECTRIC  CELL 

306.  The  Simple  Voltaic  Cell.     Experiment.     Into  a  dilute 
solution  of  sulphuric  acid  place  a  strip  of  copper  and  a  strip  of 
zinc,  so  that  they  are  a  few  centimeters  apart.     If  the  copper 
and  the  zinc  be  now  connected  by  means  of  a  wire,  as  shown  in 
Fig.  256,  a  current  of  electricity  will  flow  through 

the  wire,  as  may  be  demonstrated  by  the  ringing 
of  an  electric  bell  or  by  the  deflection  of  a  galva- 
nometer.    This  combination  of  copper,  zinc,  and 
acid  is  a  simple  voltaic  cell,  thus  named  in  honor 
of  Volta   (1748-1827),  an  Italian  physicist,   who 
was  one  of  the  first  to  experiment  with  and  de- 
scribe such  a  device.      The  essential  parts   of   a 
simple  voltaic  cell  are  two  metals  and  a  solution,  the  metals  to  be 
of  such  a  nature  that  the  solution  acts  upon  one  of  them  more 
readily  than  upon  the  other. 

A  voltaic  cell,  then,  may  be  defined  as  a  device  for  transform- 
ing the  energy  of  chemical  action  into  the  electrical  energy  of 
a  current. 

307.  Terms  Used  in  Connection  with  the  Electric  Cell.     The 
solution  used  in  a  voltaic  cell  is  called  the  electrolyte.     The  two 
metals  are  the  electrodes.     That  portion  of  an  electrode  which 
is  immersed  in  the  solution  is  sometimes  called  the  plate,  and 
the  portion  to  which  the  wire  is  attached,  the  pole.     The  elec- 
trode which  becomes  positively  charged  is  the  positive  electrode; 
the  one  negatively  charged  the  negative  electrode.     The  electrode 
which  is  least  affected  chemically  is  usually  the  positive  elec- 


198  HIGH  SCHOOL   PHYSICS 

trode;  the  one  most  affected  chemically  the  negative  electrode. 
For  example,  in  the  case  of  the  cell  described  in  the  preceding 
topic,  the  copper  is  the  positive  electrode,  the  zinc  the  nega- 
tive. The  direction  of  the  current  through  the  wire  is  assumed 
to  be  from  the  copper  to  the  zinc;  that  is,  from  the  positive  to 
the  negative  electrode.  The  entire  path  of  the  current  is  called 
the  circuit.  That  part  outside  the  liquid  is  the  external  circuit ; 
the  part  within  the  liquid,  the  internal  circuit.  Any  part  of  the 
circuit,  as  the  wire  connecting  the  electrodes,  is  called  a  con- 
ductor. Metals  in  general  are  good  conductors.  Substances 
like  glass  and  rubber  are  poor  conductors.  A  poor  conductor  of 
electricity  is  called  an  insulator. 

A  number  of  cells  joined  together  constitute  a  battery.     A 
battery  may  consist  of  a  single  cell  or  a  number  of  cells. 

308.  Voltaic  Cells  with  Different  Electrolytes.     Experiment. 
It  must  not  be  supposed  that  in  order  to  make  a  voltaic  cell 
it  is  necessary  to  use  a  dilute  solution  of  sulphuric  acid  as  the 
electrolyte.     Any  solution,  be  it  acid,  base,  or  salt,  which  will 
act  chemically  upon  the  one  electrode  more  readily  than  upon 
the  other,  will  serve  as  an  electrolyte.     This  may  be  shown  by 
the  following  experiment.     Use  electrodes  of  copper  and  zinc, 
connecting  the  poles  to  a  galvanometer.     Dip  these  electrodes 
successively  into  the  following  solutions,  rinsing  the  electrodes 
in  water  after  each  test:    (a)  Dilute  sulphuric  acid;   (b)  dilute 
hydrochloric  acid;  (c)  dilute  acetic  acid  (vinegar);    (d)  solu- 
tion of  sodium  chloride  (NaCl) .     In  each  case  the  galvanometer 
is  deflected,  showing  that  a  current  is  set  up  by  the  cell.     If 
the  electrodes  be  thrust,  for  example,  into  an  apple,  Fig.  257,  a 
current  will  also  flow,  due  to  the  action  of  the  juices  of  the  apple 
upon  the  metals.     In  fact  almost  any  vegetable  will  act  chemi- 
cally upon  the  zinc  sufficiently  to  set  up  a  current. 

309.  Voltaic  Cells  with  Different  Electrodes.     Experiment. 
In  this  experiment  it  is  desired  to  show  that  different  substances 
may  be  used  as  electrodes.      Take  as  the  electrolyte  a  dilute 
solution  of  sulphuric  acid.     First,  use  as  electrodes  copper  and 


CURRENT  ELECTRICITY 


199 


zinc.  The  copper,  as  we  have  seen,  is  positive  to  the  zinc, 
causing  the  pointer  of  the  galvanometer  to  be  deflected  in  a 
given  direction.  Second,  use  as  electrodes  copper  and  carbon. 
The  current  now  flows  through  the  galvanometer  in  the  oppo- 
site direction;  that  is,  from  the  carbon  to  the  copper,  as  shown 
by  the  opposite  deflection  of  the  pointer.  The  copper  is  in 
this  case  the  negative  electrode.  By  similar  experiments  it 
may  be  shown  that  copper  is  positive  to  zinc  and  iron,  but 
is  negative  to  silver,  platinum,  and  also,  as  has  been  shown,  to 
carbon.  In  the  following  list  any  element,  copper  for  example, 
is  positive  to  the  elements  on  the  left  of  it  and  negative  to 
elements  on  the  right  : 

-  Zn  Fe  Cu  Ag  Pt  C  + 

Thus  iron  is  positive  to  zinc  and  negative  to  copper,  while 
copper  is  positive  to  iron,  but  negative  to  silver.  The  farther 
any  two  elements  in  the  list  are  removed  from  each  other, 
the  greater  is  the  terminal  potential  difference  of  the  cell.  In 
most  commercial  cells  zinc  and  carbon  are  used  as  electrodes. 


Pn 


FIG.  257 


FIG.  258 


310.  Potential  Difference  and  Electromotive  Force.  The 
student  is  already  familiar  with  the  idea  that  currents  of  elec- 
tricity flow  from  points  of  high  potential  to  those  of  low 
potential  in  a  manner  analogous  to  the  flow  of  water  from  a 
point  of  high  pressure  to  one  of  low  pressure,  Fig.  258.  Let 


200  HIGH  SCHOOL  PHYSICS 

us  suppose  that  the  water  flows  from  one  tank  to  the  other 
through  the  pipe  C,  and  that  the  difference  of  level  in  the 
two  tanks  is  maintained  by  the  operation  »of  the  pump  P.' 
We  may  consider  such  a  system  as  somewhat  analogous  to 
that  of  an  electric  cell,  the  difference  in  pressure  between  A 
and  B  corresponding  to  the  difference  of  potential  between 
the  electrodes  of  the  cell.  In  the  case  of  the  water  the 
difference  of  level  is  maintained  by  the  expenditure  of  energy 
through  the  agency  of  the  pump;  in  the  electric  cell  the 
difference  of  potential  is  maintained  by  the  expenditure  of 
energy  due  to  chemical  action. 

The  electromotive  force  (E.M.F.)  of  a  voltaic  cell  is  that  which 
tends  to  produce  a  current.  The  E.M.F.  of  a  cell  is  equal  to 
the  difference  of  potential  between  the  electrodes  when  the 
circuit  is  open;  it  is  equal  to  the  fall  of  potential  around  the 
entire  circuit  when  the  circuit  is  closed. 

In  connection  with  the  electromotive  force  it  is  important  to 
note  two  things:  (a)  While  we  speak  of  electric  pressure  as 
being  analogous  to  water  pressure,  it  must  be  borne  in  mind  that 
electromotive  force  is  not  force,  nor  is  it  measured  in  units  of 
force;  E.M.F.  is  measured  in  units  of  work  (ergs)  per  unit 
quantity  of  electricity  conveyed  around  the  circuit,  (b)  In  the 
second  place,  a  voltaic  cell  does  not  generate  electricity;  it 
generates  electromotive  force.  The  cell  does  not  generate 
electricity  any  more  than  the  pump  of  Fig.  258  generates 
water. 

311.  Local  Action.  Experiment.  If  a  strip  of  commercial 
zinc  be  placed  in  a  dilute  solution  of  sulphuric  acid, 
chemical  action  at  once  takes  place.  The  zinc  is  dis- 
solved, forming  zinc  sulphate  and  liberating  hydro- 
gen. The  reaction  may  be  written  Zn  +  H2S04  = 


ZnSO4  +  2H.      This   chemical  action  is   called   local 


-p,      9R,Q    action.     It  is   due  to    impurities   in  the  zinc  in  the 
form   of  tiny    particles    of    carbon,    iron,   etc.     Each 
particle    constitutes,    with  the  zinc  and  acid,  a  voltaic  cell, 


CURRENT  ELECTRICITY  201 

Fig.  259.  If  the  zinc  were  perfectly  pure  there  would  be 
no  local  action.  Local  action  is  detrimental  because  it  repre- 
sents a  useless  waste  of  zinc,  giving  rise  to  chemical  action, 
but  furnishing  no  useful  current  to  the  circuit.  It  may  be 
prevented  by  coating  the  zinc  plate  with  mercury;  that  is, 
amalgamating  the  zinc. 

312.  Effect  of  Amalgamating  the  Zinc  Plate.     Experiment. 
To  demonstrate  the  effect  of  amalgamating  the  zinc  plate, 
take  a  strip  of  commercial  zinc  and  after  cleaning  it  by  immers- 
ing it  for  a  few  moments  in  dilute  sulphuric  acid,  rub  mercury 
over  its  surface  until  the  latter  becomes  bright  and  mirror  like. 
The  impurities  in  the  zinc  are  then  covered  by  the  mercury, 
which  not  only  spreads  over  to  every  part  of  the   plate,  but 
also  penetrates  to  a  considerable  depth.      If  the  amalgamated 
plate  thus  formed  be  now  placed  in  the  acid,  no  chemical  action 
will  occur,  so  long  as  the  zinc  is  not  a  part  of  the  electrical  cir- 
cuit of  the  cell.     If,  however,  the  amalgamated  zinc  plate  be 
connected  to  the  copper  electrode  by  means  of  a  wire,  chem- 
ical action  will  at  once  take  place  between  the  acid  and  the 
amalgamated  zinc,  all  the  energy  being  now  used  to  furnish  a, 
current.     Thus  it  appears  that  amalgamating  the  zinc  plate 
prevents  local  action,  but  at  the  same  time  does-  not  hinder  in 
any  way  the  zinc  from  acting  as  the  negative  electrode  when 
connected  with  the  positive  electrode  by  means  of  an  external 
circuit. 

313.  Polarization.     Experiment.     If  we  close  the  circuit  of  a 
simple  voltaic  cell  consisting  of  dilute 

sulphuric  acid  and  electrodes  of  copper 
and  amalgamated  zinc,  bubbles  of  hy- 
drogen will  appear  in  large  numbers  on 
the  copper  electrode,  Fig.  260.  This 
appearance  of  hydrogen  on  the  posi- 
tive electrode  does  not  mean  that  the  F  26Q 
copper  is  being  dissolved  by  the  acid; 
it  does  mean,  however,  that  the  hydrogen  from  the  electrolyte 


202  HIGH  SCHOOL  PHYSICS 

is  transferred  during  the  operation  of  the  cell  from  the  solu- 
tion to  the  positive  electrode,  upon  which  it  forms  a  gaseous 
layer.  This  collection  of  H  on  the  positive  electrode  reduces 
the  E.M.F.  of  the  cell  (Supplement,  572),  thereby  cutting 
down  the  current.  When  in  this  condition  the  cell  is  said  to 
be  polarized. 

Polarization  is  the  reduction  of  the  E.M.F.  of  a  cell  due  usually 
to  the  collection  of  hydrogen  on  the  positive  electrode. 

314.  Polarization,    How    Remedied.     Polarization   is   detri- 
mental because  it  reduces  the  E.M.F.  of  the  cell.     It  may  be 
remedied  by  adding  to  the  electrolyte  an  oxidizing  agent;  that 
is,  a  substance  which  will  furnish  oxygen  to  unite  chemically 
with  the  hydrogen  on  the  electrode  and  thus  form  water,  as 
represented  by  the  chemical  equation 

2  H  +  0  =  H20 

One  of  the  most  desirable  oxidizing  agents  for  depolarizing 
purposes  is  a  solution  of  chromic  acid.  Next  in  importance 
is  a  solution  of  sodium  bichromate.  Potassium  bichromate  is 
sometimes  used;  it  is  not  so  satisfactory,  however,  as  the 
sodium  bichromate  on  account  of  the  insoluble  crystals  which 
it  forms. 

315.  Factors  that  Determine  the  E.M.F.   of  a  Cell.     The 
electromotive  force  of  a  cell  is  determined  by  three  factors: 
(a)  the  kind  of  electrodes  used,  (b)  the  nature  of  the  electro- 
lyte, and  (c)  the  temperature  at  which  the  cell  operates.     The 
E.M.F.  is  independent  of  the  size  of  the  plates.     A  cell  of  given 
materials,  such  for  example  as  zinc,  copper,  and  dilute  sul- 
phuric acid,  no  larger  than  a  lady's  thimble  will  furnish  as 
high  an  E.M.F.  as  will  a  similar  cell  having  a  volume  capacity 
of  several  gallons.     While  the  E.M.F.  of  a  cell  is  independent 
of  its  size,  nevertheless  a  large  cell  is,  in  general,  more  desirable 
than  a  small  one,  because  the  larger  the  cell  the  less  the  resist- 
ance, and  hence  the  greater  the  current,  and  also  the  larger 
the  cell  the  longer  will  its  material  last  to  furnish  a  current. 


CURRENT  ELECTRICITY  203 

KINDS  OF  CELLS 

316.  Classification  of  Cells.     There  are  many  different  types 
of  cells,  depending  on  (a)  their  form,  (b)  the  character  of  the 
electrodes,  and  (c)  the  nature  of  the  electrolyte.     In  this  text 
only  a  few  of  the  more  common  types  will  be  considered; 
namely,  the  gravity  cell,  the  Leclanche  cell,  and  the  dry  cell. 

317.  The  Gravity  Cell.     A  form  of  the  gravity  cell  is  shown  in 
Fig.  261.     The  positive  electrode  consists  of  a  piece  of  copper, 
Cu,   placed  at  the  bottom   of   the   cell. 

The  negative  electrode  is  a  piece  of  zinc, 
Zn,  of  the  crowfoot  form,  suspended  from 
the  upper  margin  of  the  battery  jar.  The 
wire  leading  from  the  copper  electrode  to 
the  pole  must  be  well  insulated. 

The  cell  is  set  up  as  follows:  Crystals 
of  copper  sulphate  are  placed  in  the 
bottom  of  the  battery  jar,  which  is  then 
filled  with  water.  A  few  drops  of  sul-  FlG.261._GravityCell 
phuric  acid  are  added  to  the  water  in 
contact  with  the  zinc.  This  acid  reacts  upon  the  zinc,  form- 
ing a  dilute  solution  of  zinc  sulphate,  which  being  lighter  than 
copper  sulphate  remains  near  the  surface.  We  thus  have 
in  the  battery  two  different  solutions;  namely,  a  saturated 
solution  of  copper  sulphate  in  contact  with  the  copper  plate, 
and  a  dilute  solution  of  zinc  sulphate  in  contact  with  the  zinc 
plate.  Batteries  of  this  type  are  called  two-fluid  batteries. 
When  the  cell  is  in  action  zinc  dissolves  from  the  negative  plate 
and  goes  into  solution;  copper  from  the  electrolyte  goes  out 
of  solution  and  is  deposited  upon  the  copper  plate.  Thus 
the  zinc  plate  grows  lighter  as  the  cell  continues  in  use,  and 
the  copper  plate  grows  heavier.  Since  there  is  no  hydrogen 
involved  in  the  operation,  no  polarization  occurs.  Herein 
lies  the  great  advantage  of  cells  of  this  type;  namely,  the  cells 
do  not  polarize.  The  gravity  cell  is  used  where  continuous 


204 


HIGH   SCHOOL  PHYSICS 


currents  are  desired,  as,  for  example,  in  the  closed  circuit  work 

of  telegraphy.     (Supplement,  573.) 

The  Daniell  cell  is  another  type  of  the  two-fluid  battery, 
differing  from  the  gravity  cell  only  in 
form,  Fig.  262.  The  copper  sulphate 
is  placed  in  the  outer  chamber  of  the 
cell;  the  zinc  plate  and  zinc  sulphate 
solution,  in  the  inner  chamber,  which 
consists  of  a  porous  cup. 

The  E.M.F.  of  both  the  gravity  and 
the  Daniell  cell  is  about  1  volt. 

318.  The  Leclanche  Cell.  This  cell 
consists  of  a  vessel,  as  shown  in  Fig. 
263,  which  contains  a  solution  of  am- 
monium chloride.  A  rod  of  carbon 
serves  as  the  positive  electrode; 
a  rod  of  zinc,  as  the  negative 
electrode.  The  positive  carbon  elec- 
trode is  placed  in  a  porous  cup  which 

is  filled  with  a  mixture  of  graphite  and  manganese  dioxide. 

The  function  of  the  manganese  dioxide  is 

to  serve  as  the  depolarizing  agent. 

This  cell  is  used  for  open  circuit  work, 

such   as  the  ringing  of    door  bells,    etc. 

The  E.M.F.  of  the  Leclanche  cell  is  about 

1.4  volts. 

319.   The  Dry  Cell.     The  so-called  dry 

cell,  Fig.  264,  is  a  modified  form  of  the 

Leclanche  cell.     In  reality  it  is  not  a  dry 

cell  at  all,  since  it  contains  a  moist  paste  sH 

consisting    of   ammonium    chloride,    zinc 

chloride,  zinc  oxide,  and  plaster  of  Paris. 

The  E.M.F.  generated  is  due  to  the  ac- 
tion of  the  ammonium  chloride  upon  the 

zinc  electrode,  which  in  this  case  forms  the  outer  wall  of  the 


FIG.  262 
Daniell  Cell 


FIG.  263 
Leclanche  Cell 


CURRENT  ELECTRICITY 


205 


cell.     The  positive  electrode  is  a  carbon  rod.     The  cell  is  her- 
metically sealed  to  prevent  evaporation. 

When  the  dry  cell  is  new  its  current-producing  power  is  high; 
with  time,  however,  its  internal  resist- 
ance increases  and  its  current  is  cut 
down  proportionally.  On  account  of 
the  cheapness  and  convenience  of  these 
cells  they  are  today  more  extensively 
used  than  any  other  type.  The  E.M.F. 
furnished  is  about  the  same  as  that  of 
a  Leclanche  cell  (1.4  volts). 


CHEMICAL  EFFECTS  OF  A  CURRENT 


FIG.  264.  — Dry  Cell 


320.    The    Dissociation    Theory.     If 

a  salt,  such  as  sodium  chloride  (NaCl), 

be   dissolved    in    water,    the   greater   part    of   it  dissociates; 

that    is,    it   breaks    up    into    parts    called   ions,    as   follows: 

+ 
NaCl    in    H20  =  Na  +  Cl.      The    symbol    for    the    sodium 

+ 
atom  with  a  +  sign  above  it,  Na,  is  called  the  positive  ion; 

+ 
Cl  is  called  the  negative  ion.     The  Na  ion  carries  a  +  charge 

of  electricity;  the  Cl  carries  a  —  charge. 

The  following  chemical    reactions   illustrate  a  few  of  the 
simpler  cases  of  ionization  of  acids,  bases,  and  salts: 


HC1      in  water  =  H  +  Cl 

KC1 

AgN03      " 

H2S04       " 

CuS04       " 


=  K  +  C1 

=  Ag  +  N03 

+       + 
=  H  +  H  +  SO4 

+  + 


206 


HIGH   SCHOOL   PHYSICS 


265 


An  electrolyte  is  a  solution,  similar  to  the  above,  which 
contains  ions.  It  will  be  noted  that  when  molecules  disso- 
ciate into  ions,  there  are  always  formed  an  equal  number  of  -f- 
and  —  charges. 

321.  The  Electrolytic  Cell.     Suppose  that  we  have  a  cell 
such  as  shown  in  Fig.  265,  consisting  of  two  similar  electrodes 

and  an  electrolyte.  Let  the  electrodes  be  of 
platinum  and  the  electrolyte  be  a  dilute  acid, 
for  example,  HC1.  Now  if  a  current  be 
passed  through  this  cell  in  a  direction  indi- 
cated by  the  arrows,  the  +  ions  will  go  with 
the  current  and  the  —  ions  will  go  against 
the  current.  The  electrode  toward  which  the 
+  ions  go  is  called  the  cathode;  the  other  electrode  the  anode. 
It  is  characteristic  of  H  ions  and  metallic  ions  to  go  with  the 
current;  negative  ions  always  go  against  the  current.  Such  a 
cell  as  here  described  is  called  an  electrolytic  cell.  It  differs 
from  a  voltaic  cell  in  this  respect:  The  voltaic  cell  is  designed 
to  furnish  a  current ;  the  electrolytic  cell  is  designed  to  electrolyze 
a  solution.  Electrolysis  is  the  process  by  which  the  ions  of  a 
solution  are  separated  by  means  of  a  current. 

322.  The  Decomposition  of  Water  by  Electrolysis.     Experi- 
ment.    In  the  decomposition  of  water  by  electrol- 
ysis we  use  a  cell  of  a  type  shown  in  Fig.  266. 

The  electrodes  are  of  platinum,  which  is  used 
because  this  metal  is  not  acted  upon  by  any  acid. 
The  electrolyte  is  a  dilute  solution  of  sulphuric 
acid  in  water.  When  the  current  passes  through 
such  a  cell,  the  H  ions  appear  at  the  cathode,  give 
up  their  positive  charges,  and  are  liberated  in  the 
form  of  gaseous  hydrogen.  Oxygen,  O,  is  liber- 
ated at  the  anode.  The  relation  of  the  volume  of 
O  to  the  volume  of  H  is  as  1:  2;  that  is,  for  every 
cubic  centimeter  of  O  liberated  at  the  anode  there  are 
cubic  centimeters  of  H  liberated  at  the  cathode. 


CURRENT  ELECTRICITY  207 

323.  Chemical  Reactions  in  Electrolysis  of    Water.      The 

chemical  reactions  which  take  place  in  the  electrolysis  of  water 
containing  sulphuric  acid  are  quite  complex,  the  nature  of  the 
reaction  depending  upon  the  E.M.F.  applied.  A  full  discus- 
sion of  this  subject  is  beyond  the  limits  of  an  elementary  text, 
it  being  sufficient  to  say  that  the  object  of  adding  sulphuric 
acid  to  the  water  is  to  increase  the  concentration  of  the  ions 
and  thus  to  make  the  solution  more  conducting. 

Decomposition  of  the  water  occurs  in  this  electrolytic  pro- 
cess largely  as  a  secondary  reaction,  as  follows:   The  acid  on 

+ 
being  added  to  the  water  is  dissociated  into  H  ions  and  SO4 

+ 
ions.     The  H  ions  are  liberated  at  the  cathode  as  hydrogen; 

the  SO4  ions  appear  at  the  anode,  giving  up  their  negative 
charges  and  liberating  oxygen,  probably  after  this  manner: 

S04  +  H20  =  H2S04  +  O 

+ 
The  sulphuric  acid  thus  formed  dissociates,  forming  new  H  and 

SO4  ions. 

324.  Electrolysis   of   Copper    Sulphate.     Consider   that   we 
have  an  electrolytic  cell,  Fig.  267,  in  which  the  electrodes  are  of 
copper  and  the  electrolyte  a  solution  of  cop- 
per sulphate,  CuSO4.     The  salt  dissociates        >^  A  7* 

as  follows:  CuSO4=  Cu+  SO4.     The  posi- 


c 


tive  ions,  Cu,  are  deposited  upon  the  cath- 
ode; the  negative  ions,  S04,  unite  with  cop-  FIG.  267 
per    ions    at    the    anode,    forming    CuSO4. 
Thus  for  every  copper  ion  discharged  from  the  solution  at  the 
cathode,  a  copper  ion  is  discharged  into  the  solution  at  the 

anode,  and  the  concentration  of  the  Cu  ions  of  the  solution 
thus  remains  constant. 

If  platinum  instead  of  copper  electrodes  are  used  the  follow- 


208  HIGH  SCHOOL  PHYSICS 

+  + 

ing  reactions  will  take  place:  At  the  cathode  Cu  ions  are  dis- 
charged, thus  copper-plating  the  platinum  of  that  electrode. 

At  the  anode  SCU  ions  are  discharged,  and  since  these  ions 
cannot  react  chemically  with  the  platinum  they  react  with  the 
water,  forming  sulphuric  acid,  H2SO4  and  liberating  O,  as  in 
the  case  of  the  electrolysis  of  water. 

325.  The  Laws  of  Electrolysis.  The  laws  governing  the 
deposition  of  ions  by  electrolysis  were  first  announced  by 
Faraday  (1791-1867)  and  are  now  known  as  Faraday's  laws 
of  electrolysis.  They  are  two  in  number  and  may  be  stated 
as  follows: 

I.  The   amount  of  a  substance  deposited  in   an  electrolytic 
cell  is  proportional  to  the  strength  of  the  current  and  to  the 
time  which  it  flows.     This  means  that  if  a  given  current  flow- 
ing through  an  electrolytic  cell  for  1  hour  deposits  1  gram  of 
copper,  then  twice  as  much  current  flowing  for  2  hours  will 
deposit  2  X  2  or  4  grams  of  copper. 

II.  //  the  same  current  flow  through  two  or  more  cells  in 
series,  the  amount  deposited  at  the  electrodes  in  each  cell  will 
be  proportional  to  the  chemical  equivalent  of  the   element  de- 
posited.    The  chemical  equivalent  of  an  element  is  its  atomic 
weight   divided   by   its   valence.     The   relation   between   the 
atomic  weight,  valence,   and  chemical  equivalents  of  a  few 
typical  elements  is  shown  in  the  following  table: 

Element        Atomic        Valence        Chemical 
weight  equivalent 

H  11  1 

O  16            2  8 

Cu  63            2  31 

Ag  107             1  107 

Thus  if  there  be  three  electrolytic  cells  connected  in  series 
containing  in  order  ions  as  follows,  H,  Cu,  Ag,  and  the  same 
current  be  passed  through  each  cell,  for  every  gram  of  hydrogen 
liberated  in  one  cell  there  will  be  deposited  in  the  second  cell 
31  grams  of  copper,  and  in  the  third  107  grams  of  silver.  Appli- 


CURRENT  ELECTRICITY 


209 


cations  of  the  laws  and  principles  of  electrolysis  in  the  arts  and 
sciences  are  very  numerous,  some  of  the  more  important  being 
stated  in  the  following  topics. 

326.  The  Electrolytic  Refining  of  Copper.  As  obtained  from 
its  ores,  copper  contains  a  number  of  impurities  which  make  it 
objectionable  for  certain  kinds  of  electrical  service.  To  remove 
these  impurities  the  electrolytic  process  of  refining  is  largely 
employed.  A  large  piece  of  impure  copper  is  suspended  as 
the  anode  in  a  bath  of  copper  sulphate,  Fig.  268;  a  small  piece 
of  pure  copper  is  used  as  the  cathode.  A  current  of  proper 
strength  is  passed  through  the  cell.  The  anode  gradually  dis- 
solves and  pure  copper  is  deposited  on  the  cathode. 


FIG.  268 


FIG.  269 


327.  Copper  Plating  and  Electrotyping.     In  copper  plating 
and  electrotyping  a  bath  of  copper  sulphate  is  employed.     A 
piece  of  copper  serves  as  the  anode.     The  object  to  be  plated 
is  suspended  as  the  cathode.     In  electrotyping  an  impression 
of  the  type  after  being  set  up  is  made  in  wax,  the  surface 
of  which  is  coated  with  fine  powdered  graphite  to  render  it  con- 
ducting.    The  wax  mold  thus  prepared  is  now  put  into  the 
bath  as  the  cathode,  and  a  suitable  deposit  of  copper  made 
upon  it. 

328.  Silver  Plating.      The  silver  plating  of  tableware,  such 
as  spoons,  knives,  forks,  etc.,  Fig.  269,  is  a  familiar  illustration 
of  the  electrolysis  of  a  silver  salt.     For  such  work  a  solution  of 
silver  cyanide  is  used  as  the  electrolyte,  since  solutions  of  this 
salt  give  a  smooth  and  compact  deposit.     The  electrolysis  of 
silver  nitrate,  AgNO3,  also  furnishes  a  standard  method  of  meas- 


210  HIGH   SCHOOL  PHYSICS 

uring  currents  of  electricity,  as  will  be  more  fully  explained 
later  (Art.  332). 

329.  The    Principle    of   the    Storage    Cell.     A   storage   cell 
embodies  the   characteristics  of  both  an  electrolytic  and   a 

voltaic  cell  in  that  it  may  be  used  over  and 
over  again  by  being  alternately  charged  and 
discharged.  While  being  charged  it  acts  as 
an  electrolytic  cell;  on  discharge  it  acts  as 
a  voltaic  cell.  The  essential  features  of  a 
cell  of  this  type  may  be  illustrated  by  means 
of  a  simple  piece  of  apparatus,  Fig.  270,  con- 
sisting of  two  strips  of  lead  immersed  in 
dilute  sulphuric  acid.  The  first  step  is  to 
charge  the  cell.  This  is  done  by  passing  a 
^  current  through  it,  during  which  process  it 

acts  as  an  electrolytic  cell.  Hydrogen  is 
liberated  at  the  cathode  and  unites  with  oxygen,  which  may 
be  in  chemical  union  with  that  electrode,  thus  reducing  it  to 
bright  metallic  lead.  Oxygen  is  liberated  at  the  anode,  uniting 
with  the  lead  to  form  a  reddish  deposit  of  lead  oxide.  The 
cell  is  now  charged,  the  anode  consisting  of  lead  oxide  and 
the  cathode  of  metallic  lead. 

The  second  step  is  to  discharge  the  battery,  during  which 
process  it  acts  as  a  voltaic  cell.  If  it  be  connected  to  an  elec- 
tric bell  the  latter  will  ring  vigorously  for  some  time;  that  is, 
until  the  cell  is  discharged.  On  discharge  the  lead  oxide  is 
the  positive  electrode,  the  metallic  lead  the  negative  electrode. 
During  discharge  the  lead  oxide  is  reduced  and  the  metallic 
lead  of  the  other  electrode  is  oxidized. 

330.  Storage  Batteries  and  their  Use.      A  storage  battery 
consists  of  one  or  more  storage  cells,  two  types  of  which  are 
now  in  general  use:  one  is  the  lead  cell,  the  other  the  Edison 
cell. 

The  commercial  form  of  the  lead  cell  is  shown  in  Fig.  271. 
The  electrodes  consist  of  two  lead  plates,  one  metallic  lead, 


CURRENT  ELECTRICITY 


211 


the  other  covered  with  lead  peroxide,  both  being  immersed  in 
a  dilute  solution  of  sulphuric  acid.  The  peroxide  plate  is  red- 
dish in  color  and  is  the  +  electrode.  The  E.M.F.  of  a  lead 
cell  is  2  volts.  Since  the  internal  resist- 
ance is  very  low,  usually  less  than  0.1 
ohm,  this  cell  is  capable  of  furnishing  a 
high  current.  The  lead  cell  should  never 
be  short  circuited. 

The  Edison  cell,  Fig.  272,  is  of  compar- 
atively recent  invention  and  is  as  yet  not 
so  thoroughly  tested  as  is  the  lead  cell. 
The  electrolyte  used  in  this  cell  consists 
of  a  dilute  solution  of  caustic  potash 
(KOH).  Nickel  is  used  as  the  +  elec- 
trode and  iron  as  the  —  electrode.  The 
E.M.F.  of  the  Edison  cell  is  1.2  volts. 

Storage  batteries  do  not,   as  is  some- 
times supposed,  store  up  electricity;  a  stor- 
age battery  is  a  device  for  storing  energy. 
On  charging  the  battery  the  energy  of  an  electric  cell  is  con- 
verted into  potential  energy  represented  by  the  oxidation  of 


FIG.  271 
Lead  Storage  Cell 


FIG.  272.  —  Edison  Storage  Cell,  showing  Nickel 
and  Iron  Electrodes 

the  positive  electrode.  Stora'ge  batteries  are  largely  used  today 
to  furnish  power  for  electric  automobiles,  and  also  in  connec- 
tion with  electric  lighting  and  power  plants. 


212  HIGH  SCHOOL  PHYSICS 

For  further  important  information  relating  to  storage  bat- 
teries, see  Supplement,  574  and  575. 

UNITS  OF  ELECTRICAL  QUANTITIES 

331.  Electrical    Units.     The    four    most    important    units 
employed  in  measuring  electrical  quantities  are  (a)  the  ohm, 
the  unit  of  resistance;    (b)  the  ampere,  the  unit  of  current 
strength;    (c)  the  volt,  the  unit  of  potential  difference  and 
E.M.F.;   and  (d)  the  coulomb,  the  unit  of  quantity. 

Nearly  all  the  units  employed  in  the  measurement  of 
electrical  quantities  have  been  named  in  honor  of  some 
celebrated  physicist  or  chemist.  The  ampere,  for  example, 
was  so  named  in  honor  of  Ampere,  a  noted  French  physicist; 
the  ohm  after  Ohm,  a  German  physicist.  Likewise  the  volt 
and  coulomb  were  named  in  honor  of  Volta  and  Cou- 
lomb, respectively,  the  former  an  Italian  and  the  latter  a 
Frenchman . 

332.  The  Ampere.     A  standard  and  fundamental  method  of 
measuring  a  current  of  electricity  is  furnished  by  the  electrol- 
ysis of  silver  nitrate,  AgNO3.      The  electrolytic  cell  employed 
is  called  a  silver  voltameter,  or  better,  a  silver  coulometer, 

since  it  measures  the  quantity  of  electric- 
ity that  passes  through  it.  One  form  of 
the  silver  coulometer  is  shown  in  Fig. 
273.  This  is  an  electrolytic  cell,  con- 
sisting of  a  platinum  bowl,  which 
J^  serves  the  double  purpose  of  containing 
the  electrolyte  and  acting  as  the  cath- 
ode. The  anode  is  a  piece  of  pure  sil- 
ver. The  electrolyte  employed  is  a  solution  of  silver  nitrate, 
prepared  according  to  standard  specifications.  The  direction 
of  the  current  is  indicated  by  the  arrows.  Silver  is  deposited 
on  the  platinum  cathode,  the  quantity  thus  deposited  being 
determined  by  weighing  the  cathode  (platinum  bowl)  both 
before  and  after  the  experiment.  We  define  the  unit  of  cur- 


CURRENT  ELECTRICITY  213 

rent  strength,  the  ampere,  in  terms  of  the  quantity  of  silver 
deposited  per  second. 

An  ampere  is  that  current  which  will  deposit  0.001118  gram  of 
silver  in  one  second. 

*  333.  The  Ohm.  Every  conductor  offers  resistance  to  a 
current.  The  unit  of  resistance  is  the  ohm,  which  is  defined  as 
the  resistance  offered  to  an  unvarying  current  of  electricity  by  a 
column  of  mercury  106.3  centimeters  in  length,  of  uniform  cross 
section,  and  having  a  mass  of  14-4521  grams,  at  a  temperature  of 
0°  C.  The  reason  for  selecting  mercury  as  the  standard  metal 
in  measuring  the  unit  of  resistance  is  (a)  that  it  has  a  high 
resistance  as  compared  with  other  metals  and  (b)  it  can  be 
obtained  in  a  very  pure  state  by  distillation. 

Ohm  discovered  that  for  a  given  conductor  the  current 
strength  is  proportional  to  the  E.M.F.  This  means  that  for  a 
given  conductor  the  resistance  is  independent  of  the  strength 
of  the  current  flowing  through  it,  provided  the  temperature 
remains  constant. 

334.  The  Volt:     The  unit  of  potential  difference  and  E.M.F. 
is  called  the  volt.     A  volt  i£the  electromotive  force  that  will  cause 
a  current  of  one  ampere  to  fl&w  through  a  resistance  of  one  ohm. 
The  difference   of  potential   applied   to   the  ordinary  incan- 
descent lamp,  for  example,  is  110  volts. 

335.  The  Coulomb.     A  coulomb  is  the  quantity  of  electricity 
conveyed  in  one  second  by  a  current  of  one  ampere.     The  current 
that  flows  through  a  16  candle  power  carbon  incandescent  lamp 
when  illuminated  to  full  candle  power  is  about  J  ampere.     A 
lamp  burning  for  4  hours  will  take  4  X  60  X  60  X  J  =  7200 
coulombs. 

MAGNETIC  EFFECTS  OF  A  CURRENT 

336.  Magnetic  Field  about  a  Current.     It  was  early  discov- 
ered that  there  existed  a  very  close  relationship  between  an 
electric  current  and  magnetic  lines  of  induction.     That  there 
exists  a  magnetic  field  about  a  wire  carrying  a  current  may  be 


214  HIGH   SCHOOL   PHYSICS 

shown  in  a  very  striking  manner  as  follows:  Pass  a  wire  through 
a  hole  in  a  piece  of  cardboard  or  a  glass  plate  upon  which  iron 
filings  have  been  sprinkled.  Now  if  the  wire  be  connected 
to  a  source  of  E.M.F.  and  a  rather  strong  current  be  passed 
through  the  circuit,  the  iron  filings  will  arrange  themselves  in 
concentric  lines  about  the  conductor,  thus  showing  that  there 
is  a  magnetic  field  about  the  wire  due  to  the  current.  The 
direction  of  the  lines  of  induction  about 
the  wire  may  be  determined  by  placing  a 
magnetic  needle  upon  the  plate,  Fig.  274. 
If  the  current  through  the  wire  be  re- 
versed the  direction  of  the  lines  of  induc- 
tion will  be  reversed,  as  shown  by  the 
reversal  of  the  needle.  The  relation  be- 
tween the  direction  of  the  current  and 
F  274  ^ne  Direction  °f  the  magnetic  lines  of 

induction  may  be  illustrated  by  grasp- 
ing the  wire  with  the  right  hand  with  the  thumb  in  the  direc- 
tion of  the  current,  in  which  case  the  fingers  will  represent  the 
direction  of  the  lines  of  induction. 

337.  Effects  of  a  Current  on  the  Magnetic  Needle.  Exper- 
iment. A  magnetic  needle  always  tends  to  set  itself  parallel 
to  the  direction  of  the  lines  of  induction  of  the  magnetic  field 
in  which  it  is  placed,  in  such  a  way  that  the  lines  may  be  con- 
ceived of  as  entering  the  S-pole  and  coming  out  the  N-pole. 
When  a  magnetic  needle  is  placed  in  the  earth's  field  it  there- 
fore takes  a  north-south  position.  Now  if  a  wire  carrying  a 
current  be  brought  near  the  needle  and  above  it,  with  a  cur- 
rent flowing  in  the  direction  indicated  in  Fig.  275,  the  needle 
will  be  acted  upon  by  two  magnetic  fields,  the  earth's  field  in 
one  direction  and  the  magnetic  field  due  to  the  wire  in  a  direc- 
tion at  right  angles  to  the  earth's  field.  Two  forces  therefore 
act  upon  the  needle,  which  takes  a  position  representing  the 
direction  of  resultant  of  these  two  forces.  When  the  wire  is 
above  the  needle,  as  shown  in  Fig.  275,  the  N-pole  is  deflected 


CURRENT  ELECTRICITY 


215 


toward  the  observer.  When  the  wire  is  below  the  needle, 
Fig.  276,  the  current  remaining  in  the  same  direction,  the 
N-pole  is  deflected  away  from  the  observer. 


FIG.  275 


FIG.  276 


338.  Rule  to  Determine  the  Direction  of  Deflection  of  the 
Needle.  Grasp  the  wire  with  the  right  hand,  the  thumb  in  the 
direction  of  the  current,  and  the  fingers  will  indicate  the  direction 
of  the  magnetic  field  about  the  wire,  Fig.  277.  The  deflection  of 
the  N-pole  will  therefore  always  be  in  the  direction  of  the 
fingers. 


B 


FIG.  277 


FIG.  278 


EXERCISES.  1.  Consider  Fig.  278  with  reference  to  direction  of  current 
and  position  of  needle.  Make  drawings  to  illustrate  the  following  cases, 
using  the  right  hand  rule  to  determine  the  deflection  of  the  N-pole  in  each 
case:  (a)  Current  in  direction  BA  and  above  needle;  (b)  current  in  direc- 
tion BA  and  below  needle. 

2.  Consider  that  the  wire  carrying  the  current,  Fig.  278,  be  placed 
beside  the  needle,  the  current  flowing  from  B  to  A.  Determine  by  the 
right  hand  rule  the  effect  on  the  needle. 


FIG.  279 
3.    Determine  the  direction  of  the  current  in  the  case  of  Fig.  279. 


216 


HIGH   SCHOOL  PHYSICS 


339.  The  Solenoid.  A  solenoid  consists  of  a  coil  of  wire  of 
several  turns,  Fig.  280,  which  carries  a  current.  When  a  cur- 
rent passes  through  the  solenoid  the  coil  acquires  the  prop- 
erties of  a  magnet,  one  face  or  end  being  an  N-pole  and  the 
other  an  S-pole. 


FIG.  280.  —  Solenoid 


FIG.  281 


Experiment.  The  polarity  of  a  solenoid  may  be  shown  as 
follows:  Pass  a  current  through  a  number  of  turns  of  insulated 
wire,  Fig.  281.  Present  one  face  of  the  coil  to  the  N-pole  of  a 
magnetic  needle;  the  needle  is  deflected  in  a  given  direction. 
Present  the  other  face  of  the  solenoid  to  the  N-pole.  The  needle 
is  now  deflected  in  an  opposite  direction.  This  shows  that  a 
solenoid  acts  like  a  magnet,  having  an  N-  and  an  S-pole. 

340.  Rule  to  Determine  the  Polarity  of  a  Solenoid.  In 
determining  the  polarity  of  a  solenoid  we  may  again  make  use 
of  the  right  hand  rule.  Grasp  one  or  more  wires  in  the  right 
hand,  the  thumb  being  in  the  direction  of  the  current,  and  the 
fingers  will  represent  the  direction  of  the  lines  of  induction, 


FIG.  282 


FIG.  283 


Fig.  282.     The  face  of  the  coil  into  which  the  lines  enter  is  the 
S-pole;   the  face  out  of  which  the  lines  come  is  the  N-pole. 

It  is  also  sometimes  convenient  to  make  use  of  a  second 
rule,  as  illustrated   in  Fig.  283.    Grasp  the  solenoid  with  the 


CURRENT  ELECTRICITY 


217 


right  hand,  the  fingers  being  in  the  direction  of 
the  current,  and  the  thumb  will  indicate  the 
position  of  the  N-pole. 

341.   The  Electromagnet.     An  electromagnet 
consists    of    a  soft   iron  bar  about   which    is 


'V 

FIG.  284  —  Electromagnet 


FIG.  285 


wrapped  a  number  of  turns  of  insulated  wire,  Fig.  284.  The 
electromagnet,  it  will  be  observed,  is  nothing  more  than  a 
solenoid  having  an  iron  core.  The  presence  of  -the  metal  core 
in  the  coil  increases  enormously  the  strength  of  the  magnetic 
field,  since  the  iron  offers  a  much  easier  path  for  the  lines  of 
induction  than  does  the  air. 
An  electromagnet  of  the  horseshoe  type  is  shown  in  Fig.  285. 

342.  Parallel  Currents.     Experiment.     If  two  conductors  be 
suspended  as  shown  in  Fig.  286,  so  that  the  lower  ends  dip  into 

mercury,  and  a  current  be  allowed 
to  flow,  as  indicated  by  the  arrows, 
we  will  have  the  condition  of  paral- 
lel currents  flowing  in  the  same 
direction.  The  wires  will  be  at- 
tracted. 

If  now  the  apparatus  be  adjusted 
so  that  the  parallel  currents  flow 
in  opposite  directions,  Fig.  287,  the 
conductors  will  repel  each  other. 

The  law  of  parallel  currents  may 
be  stated  as  follows:  Parallel  cur- 
rents in  the  same  direction  attract; 
parallel  currents  in  the  opposite  direction  repel. 

343.  Explanation   of  Attraction   and   Repulsion   of   Parallel 
Currents.     The  attraction  and  repulsion  of  parallel  currents 
may  be  understood  by  considering  the  magnetic  fields  in  the 


FIG.  286 


FIG.  287 


218 


HIGH   SCHOOL   PHYSICS 


two  cases.  Fig.  288  shows  the  magnetic  field  about  parallel 
currents  in  the  same  direction.  Many  of  the  lines  of  induction 
encircle  both  wires,  and  hence  tend  to  bring  them  together. 

In  the  case  of  magnetic  fields  due  to  parallel  currents  in  the 
opposite  direction,  Fig.  289,  the  lines  of  induction  of  the  two 
systems  are  crowded  between  the  two  conductors,  and  hence 
tend  to  force  them  apart. 


a 


FIG.  288 


FIG.  289 


FIG.  290 


ELECTRICAL  MEASURING  INSTRUMENTS 

344.  The  Galvanometer.     A  galvanometer  is  an  instrument 
for  measuring  small  currents  of  electricity. 

One  of  the  sim- 
plest forms  is 
shown  in  Fig.  290. 
When  a  current 
flows  through  the 
conductor,  the 

magnetic  needle  suspended  within  the  coil 

is  deflected.     This  is  called  a  tangent 

vanometer  because  the  strength  of 

is  proportional  to  the  tangent  of  the  angle 

of  deflection.     This  form  of  galvanometer 

is  not  at  present  used  very  extensively.     A 

much  more  common  and  convenient  type 

is  the  d'Arsonval  galvanometer,  Fig.  291. 

345.  The  d'Arsonval  Galvanometer.    Tne  p1G  291  —  D'Arson- 
general   principle  upon  which   this  instru-     val  Galvanometer 


CURRENT  ELECTRICITY 


219 


ment  works  is  shown  in  Fig.  292.  A  coil  of  fine  wire  is  sus- 
pended between  the  poles  of  a  horseshoe  magnet  in  such  a 
way  that  a  current  may  enter  at  one  point  and  leave  at  an- 
other. Now  when  the  current  flows  through  the 
coil  one  face  becomes  an  N-pole?  the  other  an 
S-pole,  and  as  a  result  the  coil  swings  about  its 
axis  due  to  the  attraction  of  its  poles  for  those 
of  the  permanent  magnet.  Attached  to  the  coil 
is  a  pointer,  or  better  still,  a  small  mirror  reflect- 
ing a  beam  of  light.  Thus,  whenever  a  current 
flows  through  the  instrument,  its  presence  is  in- 
dicated by  the  deflection  of  the  coil.  The  great 
advantage  of  the  d'Arsonval  galvanometer  over 
the  tangent  galvanometer  lies  not  only  in  the  fact 
that  the  former  is  more  compact  in  construction 
and  convenient  in  form  than  is  the  tangent  galvanometer,  but 
also  that  it  is  independent  of  the  earth's  field.  The  tangent 
galvanometer  has  to  be  set  up  in  such  a  manner  that  its  mag- 
netic needle  points  north-south.  The  d'Arsonval  instrument, 
on  the  other  hand,  having  a  very  strong  magnetic  field  of  its 
own  due  to  its  permanent  magnet,  may  be  set  up  in  any  posi- 
tion whatsoever  with  respect  to  the  earth's  field. 

The  principle  of  the  d'Arsonval  galvanometer  is  very  ex- 
tensively employed  in  the  construction  of  voltmeters  and 
ammeters,  Fig.  293. 


FIG.  292 


FIG.  293. — Ammeter  and  Voltmeter 


220 


HIGH   SCHOOL   PHYSICS 


346.  The  Ammeter.  An  ammeter  is  an  instrument  for  meas- 
uring current  strength  in  amperes.  It  is  really  a  galvanometer, 
usually  of  the  d' Arson  val  type,  having  a  coil  of  very  low  resist- 
ance. A  pointer  and  scale  is  provided,  the  latter  of  which  is 
calibrated  so  as  to  indicate  readings  in  amperes.  An  ammeter 
is  always  put  in  series  with  the  circuit,  the  current  of  which  it 
is  designed  to  measure,  Fig.  294. 


FIG.  294.  —  Ammeter  in 
Series  with  Circuit 


FIG.  295.  —  Voltmeter  in  Shunt 


347.  The  Voltmeter.  The  voltmeter  is  an  instrument  for  meas- 
uring the  difference  of  potential  in  volts.  Like  the  ammeter  it 
is  also  a  d' Arson val  galvanometer,  but  differs  from  the  ammeter 
in  the  fact  that  it  is  provided  with  a  coil  of  high  resistance  and" 
also  that  it  is  calibrated  to  give  readings  in  volts.  A  voltmeter 
is  put  in  parallel  with  the  conductor  over  which  the  potential 
difference  is  to  be  measured,  Fig.  295,  and  it  is  for  this  reason 
that  voltmeters  are  constructed  with  coils  of  high  resistance; 
that  is,  so  that  the  instrument  will  draw  only  a  relatively  small 
current  from  the  main  circuit. 


FIG.  296.  —  Resistance  Box 


FIG.  297.  —  Resistance  Coils 


CURRENT  ELECTRICITY  221 

348.  The   Resistance   Box.     In  measuring  resistance  it   is 
desirable  to  have  at  hand  a  known  resistance,  such  as  is  fur- 
nished by  the  resistance  box  shown  in  Fig.  296.     Such  a  box 
contains  a  set  of  resistance  coils.     A  resistance  coil,  Fig.  297,  is 
a  coil  of  wire  having  a  definite  known  resistance.     It  is  made 
by  winding  the  wire  in  the  form  of  a  spiral,  the  two  free  ends 
being  fastened  to  the  metal  plates  A,  B,  C,  which  in  turn  are 
set  in  the  resistance  box.   The  object  of  winding  the  wire  double 
is   to   prevent   magnetizing  effects  when   the   current   passes 
through  the  coil,  and  also  to  prevent  self-induction,  as  will  be 
explained  in  Art.  378.     The  best  modern  resistance  coils  are 
made  of  manganin  wire  (Supplement,  576),  the  resistance  of 
which  is  practically  unaffected  by  ordinary  changes  of  tempera- 
ture such  as  occur  in  the  laboratory.     These  coils  are  mounted 
in  boxes  with  their  terminals  connected  to  the  brass  plates  as 
shown.     Connection  from  one  wire  of  the  coil  to  the  next  is 
made  by  means  of  a  metal  plug.    When  the  plugs  are  all  in  place 
the  resistance  of  the  box  is  practically  zero.     When  a  plug  is 
withdrawn  from  the  box  the  resistance  offered  is  equal  to  that 
of  the  coil  beneath  the  particular  plug  withdrawn. 

Resistance  boxes  may  be  bought  with  coils  varying  in  resist- 
ance from  0.1  to  1000  ohms,  and  even  greater  ranges. 

OHM'S  LAW  AND  ITS  APPLICATIONS 

349.  The  Laws  of  Resistance.     The  resistance  of  a  conduc- 
tor depends  upon  the  following  factors:    (a)  The  length  of  the 
conductor;  (b)  its  cross  section;  (c)  kind  of  material  used;  and 
(d)  the  temperature.     The  laws  of  resistance  may  be  stated  as 
follows: 

I.  The  resistance  of  a  conductor  is  directly  proportional  to  its 
length.     For  example,  if  10  feet  of  a  given  wire  have  a  resistance 
of  1  ohm,  20  feet  of  the  same  wire  will  have  a  resistance  of  2 
ohms. 

II.  The  resistance  of  a  conductor  is  inversely  proportional  to 
its  cross  sectional  area.     That  is,  the  greater  the  cross  sectional 


222  HIGH  SCHOOL  PHYSICS 

area  of  a  conductor,  the  less  the  resistance.  Since  the  cross 
sectional  area  of  a  wire  is  proportional  to  the  square  of  its  diam- 
eter d,  it  is  sometimes  convenient  to  consider  the  resistance  as 
inversely  proportional  to  the  square  of  the  diameter,  d2. 

III.  The  resistance  of  a  conductor  depends  on  the  material  of 
which  it  is  composed.     The  resistance  of  iron,  for  example,  is 
more  than  six  times  as  great  as  that  of  copper,  for  the  same 
length  and  cross  section. 

IV.  The  resistance  of  a  metallic  conductor  increases  as  the 
temperature  increases.     The  hotter  a  wire  becomes,  the  greater 
is  its  resistance.     On  the  other  hand,  the  resistance  of  carbon 
and  electrolytes  decreases  as   the  temperature  increases.     The 
resistance  of  the  carbon  filament  of  a  110  volt  16  candle  power 
incandescent  lamp  is,  when  cold,  about  440  ohms;   when  hot 
(incandescent)  about  220  ohms. 

350.   Discussion  of  the  Lav/s  of  Resistance.     The  first  three 
laws  may  be  expressed  in  the  form  of  an  equation  as  follows  : 


in  which  R  is  the  resistance  in  ohms,  I  the  length  in  feet,  d  is 
the  diameter  of  the  wire  usually  expressed  in  thousandths  of 
an  inch,  and  k  a  constant  depending  on  the  nature  of  the 
material  of  which  the  conductor  is  composed.  The  con- 
stant k  is  usually  expressed  in  ohms  per  "  mil-foot,"  a  mil- 
foot  representing  a  wire  1  foot  in  length  and  joW  of  an  inch 
in  diameter. 

The  following  are  some  values  for  k  in  ohms  per  mil-foot, 
taking  the  resistance  of  1  mil-foot  of  silver  at  20°  C.  as  9.5  ohms. 

Silver,  9.5  ohms  per  mil-foot       Platinum,  70  ohms  per  mil-foot 
Copper,  10.2  ohms  per  mil-foot  Manganin,  215  ohms  per  mil-foot 
Iron,  61.5  ohms  per  mil-foot       Mercury,  570  ohms  per  mil-foot 

Example.     Find  the  resistance  of  1000  feet  of  No.  20  copper 
wire  having  a  diameter  of  0.03  inch.     Solution:  R  =  k  X      ;  k 


CURRENT  ELECTRICITY  223 

for  copper  from  table  above  =  10.2;  I  =  1000  feet;  since  .03  inch 
on  i  n  o  \x  i  nnn 

3°  mils>  d  =  3°  and  d'  =  900'    Hence  R= 


90Q 
=  11.33  ohms. 

351.  Resistance  of  Conductors  in  Series.  When  conductors 
are  joined  end  to  end  as  shown  in  Fig.  298,  they  are  said  to  be 
connected  in  series.  The  resistance  of  a  number  of  conductors 
connected  in  series  is  equal  to  the  sum  of  the  individual  resist- 
ances; thus,  R  =  TI  +  r2  +  r3  .  .  . 

Example.  Three  wires  having  resistances  of  5,  10,  and  15 
ohms  respectively  are  connected  in  series.  Find  the  total 
resistance  of  the  combination.  Solution  :  R  =  5  +  10  +  15  = 
30  ohms. 


FIG.  298.  —  Conductors  in  Series      FIG.  299.  —  Conductors  in  Parallel 

352.  Resistance  of  Conductors  in  Parallel.     When  two  or 
more  conductors  are  connected  as  shown  in  Fig.  299  they  are 
said  to  be  in  parallel.     It  may  be  demonstrated  that  the  re- 
sistance R  of  two  or  more  conductors   in  parallel    may   be 
expressed  by  an  equation  of  the  following  form: 

---+-+- 

ft      iT»i  +  r,- 

Example.     Let  n,  Fig.  297,  be  a  resistance  of  5  ohms,  r2 
10  ohms,  and  r3  15  ohms.     Find  the  resistance  of   the  three 

wires  thus  connected  in  parallel.     Solution :  »  =  "?  +  Tri  +  TK» 

fC         O          1U          lO 

hence  R  =  2.7  ohms. 

353.  Ohm's  Law.     One  of  the  most  important  generaliza- 
tions in  electricity  is  that  known  as  Ohm's  law,  which  may 
be  stated  as  follows:   The  current  in  amperes,  I,  is  equal  to  the 


224  HIGH  SCHOOL  PHYSICS 

electromotive  force  in  volts,  E,  divided  by  the  resistance  in  ohms,  R. 
The  equation  for  this  law  is 

I-* 

"  R 

which  implies  that  the  current  from  any  source,  such  as  a  bat- 
tery, is  directly  proportional  to  the  voltage  and  inversely  pro- 
portional to  the  resistance;  that  is,  for  a  given  resistance  the 
greater  the  E.M.F.  the  greater  the  current;  and  on  the  other 
hand,  for  a  given  E.M.F.  the  greater  the  resistance  the  less  the 
current. 

354.  Current  Strength  in  a  Circuit.  We  learn  from  Ohm's 
law  that,  so  far  as  direct  currents  are  concerned,  there  are  only 
two  ways  of  increasing  or  decreasing  a  current,  and  that  is  by 
changing  either  E  or  R.  If  a  given  electromotive  force  E  be 
applied  to  a  circuit,  then  the  current  strength  depends  entirely 
upon  the  value  of  the  resistance  R.  It  is  important  to  note  in 
this  connection  that  when  the  values  of  E  and  R  are  once 
fixed,  the  current  strength  is  the  same  in  all  parts  of  the  cir- 
cuit. Thus  if  ammeters  A  and  A'  be  placed  in  the  same 
circuit,  Fig.  300,  it  will  be  found  that,  for  a  given  electromo- 
tive force  and  resistance,  the  current  strength,  as  registered  by 
the  instrument,  will  be  the  same  at  both  points. 


B 
FIG.  300  FIG.  301 

355.    Fall  of  Potential  by  Ohm's  Law.     Ohm's  law  may  be 
stated  in  a  very  convenient  form, 

E  =  IE 

in  which  E,  the  fall  of  potential  between  two  points  on  the 
conductor,  is  equal  to  the  product  of  the  current  flowing  through 


CURRENT  ELECTRICITY  225 

the  conductor  multiplied  by  the  resistance  of  the  conductor  be- 
tween the  given  points.  This  equation  contains  three  factors; 
therefore,  when  two  of  these  quantities  are  given,  the  third 
may  readily  be  found.  Ohm's  law,  then,  furnishes  a  standard 
method  of  determining  (a)  the  fall  of  potential  between  the 
two  points  and  (b)  the  resistance  of  a  conductor. 

Example.  To  illustrate  the  use  of  this  equation,  let  us  con- 
sider the  conductor  shown  in  Fig.  301.  The  current  /  flowing 
through  the  wire  is  2  amperes;  the  resistance  of  the  conductor 
from  A  to  B  is  5  ohms.  The  fall  of  potential  therefore  is  E  = 
IR  =  2  X  5  =  10  volts,  which  is  the  value  registered  by  the 
voltmeter. 

356.  Fall  of  Potential  over  Conductors  in  Parallel.  Sup- 
pose that  water  flow  from  a  point  A  through  three  trenches  to 
a  point  B  on  a  lower  level.  Now  while  the  trenches  may 
extend  from  A  to  B  by  entirely  different  paths  and  the  water 
flowing  in  any  trench  may  be  entirely  different  in  quantity 
from  that  of  any  of  the  other  trenches,  yet  we  readily 
comprehend  that  the  difference  of  pressure  between  the 
two  points  A  and  B  is  the  same,  no  matter  what  path 
we  consider.  Suppose  now  that  a  current  from  a  point 
A  at  high  potential  flow  over  three  paths  or  conductors 
to  a  point  B  of  low  potential.  As  in  the  case  of  the  trenches, 
the  conductors  may  be  quite  different  in  length  and  the 
currents  of  electricity  flowing  in  each  may  also  differ  from 
each  other,  yet  the  fall  of  potential  from  A  to*B  is  the  same, 
no  matter  which  path  we  consider.  That  is,  in  the  case  of  con- 
ductors in  parallel  the  fall  of  potential  over  each  conductor  is 
the  same,  and  furthermore,  the  fall  of  potential  over  each  con- 
ductor is  the  same  as  the  fall  of  potential  from  A  to  B  obtained 
by  multiplying  the  total  current  by  the  total  resistance  between 
these  points. 

Example.  Three  conductors,  4,  6,  and  12  ohms  respectively, 
connect  the  points  A  and  B.  A  current  of  6  amperes  flows  from 
A  to  B,  a  part  passing  through  each  conductor.  Find  (a)  the 


226 


HIGH   SCHOOL  PHYSICS 


fall  of  potential  from  A  to  B ;  (b)  the  current  through  each  wire. 
Solution :  (a)  The  current  from  A  to  B  =  6  amperes;  the  resist- 
ance from  A  to  B  =  2  ohms.  Therefore,  the  fall  of  potential 
from  AtoB  =  6X2  =  12  volts,  (b)  Now  since  the  fall  of 
potential  from  A  to  B,  as  just  found,  is  12  volts,  the  fall  of  poten- 
tial over  any  one  of  the  three  paths  is  also  12  volts.  Hence  the 
current  in  the  first  path  will  be  -V  =  3  amperes;  the  current  in 
the  second  path  V  =  2  amperes;  the  current  in  the  third  path 
if  =  1  ampere.  The  total  current  in  all  three  paths  =  3  +  2 
+  1=6  amperes. 

357.  Resistance  by  Ohm's  Law.  The  equation  E  =  IR 
suggests  also  a  method  of  determining  the  resistance  of  a  con- 
ductor, provided  the  current  I  and  the  voltage  E  be  known; 
thus,  R  =  E/I.  In  order  to  find  E  and  /  experimentally  it  is 
necessary  to  use  the  voltmeter  and  the  ammeter;  for  this  reason 
the  method  is  sometimes  spoken  of  as  the  voltmeter-ammeter 
method  of  measuring  resistance. 

Example.  Suppose  we  desire  to  find  the  resistance  of  a  lamp 
by  the  voltmeter-ammeter  method.  An  ammeter  is  put  in 
series  with  the  lamp  and  a  voltmeter  connected  across  its  ter- 
minal, Fig.  302.  The  reading  of  the  ammeter  is  J  ampere 
and  that  of  the  voltmeter  110  volts.  Find  the  resistance  of 
the  lamp.  Solution :  R  =  E/I  =  220  ohms. 


FIG.  303 


FIG.  302 


FIG.  304 


CURRENT  ELECTRICITY 


227 


EXERCISES.    4.   Find  the  resistance  of  10  miles  of  iron  telephone  wire 
having  a  diameter  of  150  mils. 

5.  Consider  Fig.  303.     The  resistance  of  r\  is  15  ohms,  that  of  r2  10 
ohms.     Find  the  resistance  of  the  two  conductors  in  parallel. 

6.  Three  wires,  the  resistance  of  which  are  2,  4,  and  6  ohms  respect- 
ively, are  connected  in  parallel.     Find  the  resistance  of  the  system. 

7.  The  three  wires  of  exercise  6  are  connected  as  in  Fig.  304.     Find 
the  resistance  of  the  system. 

8.  Given  three  incandes.cent  lamps,  the  resistance  of  each  when  hot 
being  220  ohms.     Find  the  resistance  (a)  when  the  three  are  connected  in 
series;  (b)  when  connected  in  parallel. 

9.  Two  conductors,  r\  of  resistance  2  ohms,  r2  8  ohms,  are  put  in  paral- 
lel.    A  current  of  10  amperes  flows  through  ammeter  A,  Fig.  305.     What 
current  flows  through  (a)  ri?    (b)  through  r2?    (c)  through  ammeter  A'  ? 

10.  Find  the  fall  of  potential  over  n  of  exercise  9;   (b)  the  fall  of  poten- 
tial over  r2. 


FIG.  305 

358.  Resistance  by  the  Wheatstone  Bridge  Method.  We 
have  just  discussed  a  method  of  determining  resistance  by  the 
use  of  Ohm's  law;  that  is,  in 
determining  R  from  E  and  /. 
Another  very  useful  method  is 
known  as  the  Wheatstone  bridge 
method.  Wheatstone's  bridge, 
so  named  after  its  inventor,  Sir 
Charles  Wheatstone,  is  a  device 
for  measuring  a  resistance  by 
comparing  it  with  a  known  re- 
sistance. The  principle  of  the 
bridge  is  shown  in  Fig.  306,  in 
which  Ri,  R2,  RS)  R4  represent 

resistances.  A  galvanometer  G  is  connected  to  the  points  C 
and  D;  a  battery  to  the  points  A  and  B.  When  the  bridge 
is  in  balance,  the  fall  of  potential  (RI)  on  the  conductor  AC  is 


FIG.  306 


228  ' 


HIGH   SCHOOL   PHYSICS 


equal  to  that  along  the  conductor  AD,  and  the  fall  of  poten- 
tial along  CB  is  equal  to  that  along  DB,  no  current  flows 
through  the  galvanometer.  In  other  words,  the  bridge  is  in 
balance  when  the  galvanometer  shows  no  deflection.  When 
this  condition  is  realized,  R\:  Rz  =  R^:  R*. 

A  simple  demonstration  of  the  principle  of  the  bridge  may  be 
shown  by  means  of  Fig.  307.     Suppose  that  it  is  desired  to  find 

the  resistance  of  the  coil  of  wire  X. 
Three  resistance  boxes,  Ri,  RS)  R*, 
are  placed  in  the  three  arms  of  the 
bridge  as  shown,  X  being  the  fourth 
arm.  Let  the  resistance  in  R3  be  10 
ohms  and  that  in  Ri  100  ohms.  We 
now  adjust  the  resistance  in  Ri  until 
the  bridge  is  in  balance;  that  is, 
until  the  galvanometer  shows  no  deflection.  Suppose  that  Ri 
is  25  ohms,  then  by  means  of  the  equation  we  now  find  the 
value  of  X  as  follows: 

Ri:X  =  R3:R* 
25:  X  =  10:100 
X  =  250  ohms 

In  order  to  avoid  the  use  of  three  resistance  boxes  and  also 
to  facilitate  the  adjustment  of  the  bridge,  a  device  known  as 


r 

R 

1 

X 

rl          ®           i 

L 

.R 

I 

R 

—  ' 

K 

FIG. 

B 

307 

FIG.  308.  —  Slide  Wire  Bridge 

a  slide  wire  bridge  is  used,  Fig.  308,  in  which  only  one  resist- 
ance box  is  required,  a  divided  wire  taking  the  place  of  the 
other  two. 

359.    Methods  of  Joining  Cells.     Ohm's  law  may  be  applied 
to  determine  the  best  method  of  joining  the  cells  of  a  battery. 


CURRENT  ELECTRICITY 


229 


The  current  furnished  by  a  battery  of  one  or  more  cells  is  deter- 
mined by  the  electromotive  force  E  and  by  the  resistance  of  the 
system.  The  resistance  of  a  coil  is  made  up  of  two  parts,  that 
of  the  wires,  etc.,  connected  to  the  poles,  called  the  external 
resistance  R,  and  that  of  the  battery  itself,  called  the  internal 
resistance  r.  The  internal  resistance  of  a  battery  depends 
upon  the  nature  of  the  materials  of  which  it  is  made,  including 
electrodes  and  electrolyte,  and  upon  the  size  of  the  plates; 
the  larger  the  plates  the  less  the  resistance.  It  is  important  to 
keep  in  mind,  in  this  connection,  the  fact  that  the  E.M.F.  of  a 
cell  is  independent  of  the  size  of  the  plates. 

The  cells  of  a  battery  may  be  connected  in  two  ways: 
(a)  in  series  and  (b)  in  parallel. 

360.  Cells  in  Series.  When  cells  are  set  up  in  series  the  con- 
necting wires  join  positive  pole  to  negative  pole,  as  shown  in 


FIG.  309.  —  Cells  in  Series 


FIG.  310 


Fig.  309.     A  diagrammatic  representation  of  cells  in  series  is 
shown  in  Fig.  310.     By  Ohm's  law  the  current  furnished  by 

''B7 

>  in  which  R  is  the  external  resistance  and 


one  cell  is  /  =        .     > 
R  +  r 

r  the  internal  resistance  of  the  cell;  for  n  cells  joined  in  series 
I  =  ^"T  —  '•     Thus  the  effect  of  joining  cells  in  series  is  to 

make  the   total   electromotive   force  and   internal   resistance 
respectively  n  times  that  of  a  single  cell. 

361.  Cells  in  Parallel.  When  cells  are  connected  in  parallel, 
all  the  positive  electrodes  are  joined  together,  and  likewise  all 
the  negative  electrodes,  Fig.  311.  The  diagrammatic  represen- 


230 


HIGH  SCHOOL  PHYSICS 


tation  of  cells  in  parallel  is  shown  in  Fig.  312.  The  effect  of 
connecting  a  battery  in  parallel  is  equivalent  to  producing 
a  single  cell,  having  an  E.M.F.  equal  to  one  of  the  original 


1 


1 


FIG.  311.  — Cells  in  Parallel 


FIG.  312 


cells,  the  plates  of  which  are  n  times  as  large  as  those  of  any  one 
of  the  original  cells  and  the  internal  resistance,  therefore, 
r/n.  Since  the  electromotive  force  of  a  battery  is  independ- 
ent of  the  size  of  the  plates,  the  E.M.F.  of  n  cells  joined  in 
parallel  is  equal  to  that  of  any  single  cell.  By  Ohm's  law, 
therefore,  we  may  write  for  n  cells  in  parallel 


R  +  r/n 

362.  The  Advantage  of  Cells  in  Series  and  in  Parallel.  The 
relation  of  the  current  /  to  the  external  resistance  R  for  cells 
connected  in  series  and  in  parallel  may  be  demonstrated  most 
satisfactorily  by  means  of  examples.  Given  three  cells  the 
electromotive  force  E  of  each  1  volt,  the  internal  resistance  r 
of  each  3  ohms. 

Example.  Find  the  current  furnished  through  an  external 
resistance  R  of  21  ohms  (a)  for  a  single  cell;  (b)  when  the 
cells  are  joined  in  series;  and  (c)  in  parallel. 

Solution  : 

(a)  Single  cell,  I  =  E/(R  +  r)  =  A  =  0.041 

(b)  Series          I  =  nE/(R  +  nr)  =  3/(21  +  9)  =  0.100 

(c)  Parallel       I  =  E/(R  +  r/n)  =  I/  (21  +  1)  =  0.045 


CURRENT  ELECTRICITY  231 

It  therefore  appears  that  when  the  external  resistance  R  is 
large  in  comparison  with  the  internal  resistance  r,  as  in  this 
case,  the  series  arrangement  gives  a  current  nearly  three  times 
as  great  as  that  of  one  cell,  while  the  parallel  method  of  join- 
ing gives  a  current  but  very  little  greater  than  that  of  a 
single  cell. 

Example.  Find  the  current  furnished  through  a  resistance 
R  of  0.1  ohm  (a)  for, a  single  cell;  (b)  when  the  cells  are  con- 
nected in  series;  (c)  in  parallel. 

Solution : 

(a)  Single  cell,  I  =  E/(R  +  r)  =  1/3.1  =  0.32 

(b)  Series         I  =  nE/(R  +  nr)  =  3/9.1  =  0.33 

(c)  Parallel      I  =  E/(R  +  r/n)  =  1/1.1  =  0.91 

It  is  evident  from  a  consideration  of  the  above  examples  that 
when  the  external  resistance  R  is  less  than  the  internal  resistance 
r  of  a  single  cell,  the  method  of  joining  cells  in  parallel  is  to  be  pre- 
ferred. Since,  however,  the  external  resistance  is  nearly  always 
greater  than  the  internal  resistance,  cells  are  almost  without 
exception  connected  in  series.  (Supplement,  577.) 

•« 

HEATING  EFFECT  OF  A  CURRENT 

363.   The  Electric  Current  as  a  Heating  Agent.     Whenever 
a  current  of  electricity  flows  through  a  conductor  heat  is  devel- 
oped.      The    case 
that  is  most  famil- 
iar is  that  of  the  FlG   314 
heating  of  the  fila- 
ment of  an  incandescent  lamp.     Other  illus- 
trations of  the  heating  effect  of  a  current  are 
FIG.  313           exemplified  in  the  use  of  the  electric  flatiron, 
Fig.   313,   the   electric    soldering    iron,   Fig. 
314,  and  similar  appliances.     Electric  currents  are  also  used 
in  some  places  for  cooking,  and  occasionally  for  the  heating 
of  rooms. 


232  HIGH   SCHOOL  PHYSICS 

364.  The  Laws  of  Heat  Development  by  a  Current.     By 
means  of  a  simple  calorimeter,  Fig.  315,  in  which  a  current  of 
electricity  was  passed  through  a  wire  immersed  in  a  nonconduct- 
ing fluid,  Joule  was  able  to  determine  the  relation 
of  the  number  of  heat  units  H,  developed  by  the 
current  /  flowing  through  a  resistance  R  in  the 
time  t.     This  relation  is  expressed  in  the  follow- 
ing laws:  % 

I.  The  heat  is  proportional  to  the  time  which  the 
current  flows. 

II.  The  heat  is  proportional  to  the  resistance  of 
the  conductor. 

III.  The  heat  is  proportional  to  the  square  of  the 
current.     That  is,  if  a  current  of  1  ampere  develops 

1  unit  of  heat  per  second,  then  a  current  of  2  amperes  will 
develop  4  units  of  heat  per  second. 

These  laws  may  be  expressed  by  the  equation 

H  =  I2  X  R  X  t  X  0.24 

in  which  H  is  the  heat  in  calories,  I  the  current  in  amperes, 
R  the  resistance  in  ohms,  and  t  the  time  in  seconds.  The  con- 
stant 0.24  was  determined  by  experiment  and  is  the  factor  by 
which  it  is  necessary  to  multiply  in  order  to  express  the  result  in 
calories. 

Example.  A  current  of  2  amperes  flows  through  a  conduc- 
tor having  a  resistance  of  5  ohms  for  10  minutes.  Find  the 
heat  developed  in  calories. 

Solution : 

H  =  P  X  R  X  t  X  0.24  =  4X5X10X60X  0.24 
=  2880  calories. 

365.  The  Incandescent  Lamp.     At  the   present  time  the 
most  important  commercial  application  of  the  heating  effect 
of  a  current  is  in  the  production  of  light,  as  in  the  case  of  incan- 
descent and  arc  lighting  systems.     In  the  incandescent  lamp 


CURRENT  ELECTRICITY 


233 


a  filament  of  some  nonfusible  substance  is  enclosed  within  a 
glass  bulb,  from  which  the  air  is  thoroughly  exhausted.  The 
object  of  removing  the  air  from  the  bulb  is  twofold:  (a)  it  pre- 
vents the  burning  out  of  the  filament  due  to  the  presence  of 
oxygen,  and  (b)  it  prevents  conduction  of  heat  from  the  fila- 
ment to  the  glass.  In  a  vacuum  very  much  less  heat  is  trans-» 
mitted  from  the  incandescent 
filament  to  the  glass  bulb  than 
would  be  the  case  if  a  gas  were 
present;  for  this  reason  the  more 
nearly  perfect  the  vacuum,  the 
greater  the  intensity  of  the  light. 

The    incandescent    lamps    are  j?IG  3^5 

used  mainly  for  indoor  lighting, 

although  in  some  cases  they  are  employed  for  street  lighting 
purposes,  Fig.  316. 

The  essential  parts  of  an  incandescent  lamp  are  shown  in 
Fig.  317.  The  current  is  conducted  to  and  from  the  lamp  by 
means  of  copper  wires  cc.  It  is  conducted 
through  the  glass  by  means  of  short  platinum 
wires  pp,  which  are  somewhat  exaggerated  in 
the  figure  for  purposes  of  illustration.  The 
object  of  using  platinum  is  that  this  metal  has 
the  same  coefficient  of  expansion  as  glass,  and 
therefore  may  be  sealed  into  glass  without 
cracking  the  latter  on  cooling.  The  filament 
consists  of  some  nonfusible  substance  which 
in  being  heated  to  incandescence  furnishes  the 
light. 

There  are  at  present  on  the  market  two 
general  types  of  incandescent  lamps:  (a)  those  having  car- 
bon filaments,  Fig.  318,  and  (b)  those  having  metal  filaments, 
as  for  example,  tungsten,  Fig.  319. 

366.    Comparison  of  Carbon  and  Tungsten  Lamps,     (a)  The 
filament  of  a  carbon  incandescent  lamp  consists  of  an  espe- 


FIG.  317 


234 


HIGH  SCHOOL  PHYSICS 


FIG.  318 


FIG.  319 


cially  prepared  thread  of  carbon;  that  of  the  tungsten  lamp  is 
made  of  tungsten,  a  metal  which  is  capable  of  being  drawn 
out  into  fine  flexible  wires  and  which  may  be  heated  to  incan- 
descence without  melting,  (b)  The 
carbon  filament  lamp  is  somewhat 
the  cheaper  of  the  two,  but  for  a 
given  current  its  candle  power  is 
considerably  less  than  that  of  the 
tungsten  lamp.  It  has  been  dem- 
onstrated experimentally  that  when 
two  given  lamps  are  consuming  the 
same  amount  of  electrical  energy, 
the  candle  power  of  the  tungsten 
lamp  is  nearly  three  times  that  of 

the  carbon  lamp.  For  example,  a  16  candle  power  carbon 
lamp  on  a  110  volt  circuit  takes  a  current  of  about  J  am- 
pere. The  power  expended  (El)  is  therefore  J  X  110  =  55 
watts.  The  expenditure  of  energy  of  such  a  lamp  per  candle 
power  is  therefore  55/16  =  3.4  watts  per  candle  power.  Now  a 
40  watt  tungsten  lamp  gives  about  32  candle  power;  hence  its 
expenditure  of  energy  is  40/32  =  1.25  watts  per  candle  power, 
(c)  The  life  of  a  carbon  lamp  is  about  800  hours;  that  of  a 
tungsten  lamp,  barring  accidents  such  as  breakage  of  globe  or 
filament,  an  indefinite  number  of  hours,  (d)  A  carbon  lamp 
has  an  advantage  in  that  it  may  be  moved  about  freely 
and  subjected  to  jars,  while  incandescent,  without  injury;  the 
tungsten  lamp,  on  the  other  hand,  cannot  be  subjected  to 
very  rough  treatment  while  incandescent,  since  there  is  danger 
of  injuring  the  metal  filaments  which  are  quite  soft  while  hot. 
367.  Incandescent  Lamp  Circuits.  Incandescent  lamps  are 
in  general  connected  in  parallel  between  the  mains  which 
lead  from  the  dynamo  (direct  or  alternating)  or  from  the  low 
voltage  side  of  a  transformer  (Art.  392).  The  method  of  con- 
necting incandescent  lamps  hi  parallel  is  shown  in  Fig.  320. 
Each  lamp  of  a  circuit  may  be  turned  on  or  off  by  means  of  a 


CURRENT  ELECTRICITY 


235 


key  in  the  socket;  all  the  lamps  of  the  circuit  may  be  turned 
on  or  off  by  means  of  a  switch  S.  The  resistance  of  the  incan- 
descent lamp  is  comparatively  high,  that  of  the  16  candle  power 


MAINS  LEADING 
TO  DYNAMO  OR 
TRANSFORMER 


FIG.  320 

1 10  volt  carbon  filament  lamp  being,  when  hot,  about  220  ohms. 
When  the  lamps  are  connected  in  parallel  the  resistance  of  the 
system,  however,  is  very  materially  reduced.  Also,  when  the 
lamps  are  in  parallel  one  or  more  may  be  turned  off  without 
seriously  disturbing  the  rest  of  the  circuit. 

368.  The  Arc  Lamp.  The  essential  features  of  an  arc  lamp 
consist  of  two  sticks  of  carbon,  the  ends  of  which  touch.  When 
a  current  is  passed  through  the  line  the 
carbon  points  are  drawn  apart  for  a  short 
distance,  usually  by  means  of  an  electro- 
magnet connected  with  the  lamp.  (Supple- 
ment, 578.)  The  current  passes  across  the 
air  gap  there  formed  and  heats  the  tips  of 
the  carbons  to  incandescence.  One  carbon, 
Fig.  321,  is  called  the  positive  carbon  and 
the  other  the  negative.  In  the  space  be- 
tween the  carbons  there  is  formed  a  volatil- 
ized carbon  arc  which  serves  as  a  conductor 
from  one  point  to  the  other;  it  is  called  the 
electric  arc  because  of  its  curved  shape. 
The  positive  carbon  is  very  much  the  hot- 
ter of  the  two  and  furnishes  the  greater 
part  of  the  light.  In  the  positive  carbon 
there  is  a  depression  which  is  called  the  crater.  The  temper- 
ature of  this  crater  when  the  lamp  is  heated  is  about  3500°  C., 
which  is  probably  the  highest  temperature  attainable  by  pres- 
ent methods. 


FIG.  321 
Electric  Arc 


236 


HIGH   SCHOOL  PHYSICS 


FIG.  322 


369.  Arc  Lamp  Circuits.     In  operating  arc  lighting  systems 
the  lamps  are  put  in  series,  as  indicated  by  the  diagram  of 
Fig.  322.     If  one  lamp  should  go  out  provision  is  made  that 

the  current  be  conducted  around  it 
by  an  automatic  device,  thus  pre- 
venting all  the  lamps  on  the  circuit 
being  put  out  of  commission.  The 
ordinary  arc  lamp  requires  a  differ- 
ence of  potential  between  the  car- 
bons of  about  50  volts;  the  current 
required  to  operate  the  lamp  is  from  4  to  10  amperes. 

370.  Kinds  of   Arc  Lamps.     In  the  open  arc  the  carbons 
burn  in  the  air.     In  this  case  the  positive  carbon  wastes  away 
about  twice  as  fast  as  the  negative,  and  both  are  consumed 
much  more  rapidly  than  if  they  were  enclosed  in  some  non- 
combustible  medium.     To  add  to  the  length  of  life  of  the 
carbon,  the  so-called  enclosed  arc  lamp  is  employed. 

In  the  enclosed  arc  lamps,  Fig.  323,  the  carbons  are  placed 
within  a  small  globe  which  is  nearly  air  tight.  After  the  lamp 
has  been  burning  for  a  short  time  all  the  oxy- 
gen within  the  globe  is  consumed,  and  the  car- 
bons then  burn  in  an  oxygen  free  gas,  mainly 
carbon  dioxide.  In  this  form  of  arc  lamp  the 
consumption  of  the  carbon  is  very  materially 
decreased,  but  the  luminous  efficiency  of  the 
lamp  is  also  decreased. 

The  flaming  arc.  In  the  ordinary  arc  lamp 
described  above  most  of  the  light  comes  from 
the  positive  carbon,  very  little  being  given  out 
by  the  arc.  In  lamps  of  the  flaming  arc  type 
the  carbons  contain  a  mixture  of  lime,  mag- 
nesia, and  other  substances,  which  give  to  the 
arc  its  brilliant  flaming  character.  In  such  lamps  the  arc 
itself  is  the  chief  source  of  light. 

371.  Fuse  Wires  and  Plugs.     Advantage  is  taken  of  the 


FIG.  323 


CURRENT  ELECTRICITY  237 

heating  effect  of  a  current  in  the  manufacture  of  fuse  wires 
and  plugs,  which  are  devices  for  automatically  breaking  the 
circuit  in  case,  for  a  given  system,  the  current  becomes  dan- 
gerously high.  Fuse  wires  and  fuse  plugs  are  made  of  some 
high  resistance  material  which  has  a  low  melting  point.  The 
fuse  plug,  Fig.  324,  is  so 
constructed  as  to  be  easily 
slipped  in  or  out  of  a  cir- 
cuit. It  consists  of  a  FIG.  324.  — Fuse  Plug 
high  resistance  conduc- 
tor of  such  a  nature  that  it  will  melt  at  a  given  current 
strength  and  thus  break  the  circuit.  Suppose,  for  example, 
that  a  fuse  wire  or  plug  be  placed  in  a  circuit  containing  a  piece 
of  apparatus,  the  maximum  carrying  capacity  of  which  is  2.5 
amperes,  but  which  is  designed  to  be  operated,  under  ordi- 
nary conditions,  with  a  current  of  2  amperes  or  less.  If  now 
for  any  reason  the  current  should  tend  to  rise  above  the  carry- 
ing capacity  of  the  instrument,  the  fuse  wire  would  melt  at 
2  amperes  and  thus  save  the  apparatus  from  burning  out. 

In  dwelling  houses  in  which  an  incandescent  lighting  system 
is  used  there  is,  in  general,  a  fuse  box  containing  fuse  wires  or 
plugs  for  each  division  of  the  lighting  circuit.  The  capacity  of 
these  fuses  is  usually  from  5  to  10  amperes;  that  is,  they  are 
designed  to  melt  when  the  current  much  exceeds  these  values. 
Since  the  melting  or  "  blowing  "  of  a  fuse  is  always  accom- 
panied by  the  formation  of  an  electric  arc  which  is  likely  to 
set  fire  to  nearby  inflammable  material,  fuses  should  always 
be  enclosed  in  fireproof  receptacles. 

POWER  EXPENDED  BY  A  CURRENT 

372.  Electric  Power.  The  power  expended  by  the  electric 
current  is  expressed  in  watts,  or  more  often  in  kilowatts.  A 
watt,  as  defined  in  mechanics,  represents  the  expenditure  of  energy 
at  the  rate  of  10}000,000  ergs  per  second;  a  kilowatt  is  1000 
watts.  In  order  to  determine  the  power  expended  by  an  elec- 


238 


HIGH  SCHOOL  PHYSICS 


trie  current  it  is  necessary  to  know  two  things:  (a)  the  current 
strength,  (b)  its  voltage.     This  relation  may  be  expressed  as 

watts  =  volts  X  amperes  =  El 

It  must  be  borne  in  mind  that  when  we  speak  of  the  watt 
and  the  kilowatt  these  terms  refer  to  units  of  power,  which 
represent  the  expenditure  of  energy  per  unit  of  time.  A  40 
watt  lamp  is  a  lamp  which  consumes  electrical  energy  at  the 
rate  of  40  watts;  that  is,  400,000,000  ergs  per  second. 

373.  The  Expenditure  of  Electrical  Energy  by  a  Current. 
Since  the  watt  and  kilowatt  represent  the  expenditure  of  energy 
per  second,  it  follows  that  if  we  desire  to  find  the  total  energy 
expended  by  a  current  in  a  given  time,  we  must  multiply  the 
power  (watts  or  kilowatts)  by  the  time  which  the  current 
flows.  The  units  thus  employed  to  express  the  total  energy 
expended  are  the  watt  hour  and  kilowatt  hour.  A  watt  hour 

represents  an  expenditure  of 
energy  at  the  rate  of  one  watt 
for  one  hour.  Since  1  watt  is 
equivalent  to  10,000,000  ergs 
per  second,  a  watt  hour  is 
therefore  equal  to  10,000,000 
X  60  X  60  ergs  =  36  X  109  ergs. 
374.  The  Watt-Hour  Meter. 
The  watt-hour  meter  is  an  in- 
strument for  summing  up  the 
total  energy  delivered  to  an 
electric  circuit.  Such  meters 
may  be  made  to  operate  on 
either  direct  or  alternating 
currents.  The  mechanism  of 
FIG. 325. -Kilowatt-hour  Meter  a  watt-hour  meter  is  essen- 
tially that  of  a  small  motor, 

the  armature  of  which  revolves  at  a  speed  proportional  to  the 
rate  at  which  electrical  energy  is  passing  through  it.     The 


CURRENT  ELECTRICITY  239 

armature  is  geared  to  recording  dials,  arranged  like  the  dials 
on  a  gas  meter  which  register  the  number  of  kilowatt  hours 
of  energy  which  pass  through  the  meter. 

The  instrument  shown  in  Fig.  325  records  the  electrical 
energy  in  kilowatt  hours. 

Example.  A  current  of  J  ampere  under  a  pressure  of  110 
volts  flows  through  an  incandescent  lamp  for  5  hours,  (a) 
Find  the  power  expended  in  watts,  (b)  Find  the  energy  ex- 
pended in  watt  hours,  (c)  Find  the  energy  expended  in  kilo- 
watt hours,  (d)  Find  the  total  energy  expended  in  ergs. 

Solution:  (a)  Watts  =  El;  hence  110  X  i  =  55  watts,  (b) 
Watt  hours  =  watts  X  time  in  hours  =  55  X  5  =  275  watt 
hours,  (c)  1  kilowatt  =  1000  watts;  therefore  275  watt  hours  = 
0.275  kilowatt  hour,  (d)  1  watt  represents  the  expenditure  of 
energy  of  10,000,000  ergs  per  second;  hence  the  total  energy  ex- 
pended in  ergs  =  55  X  5  X  60  X  60  X  10,000,000  =  99  X  1011 
ergs. 

EXERCISES:  11.  Given  an  incandescent  lamp  of  220  ohms  resistance 
across  the  terminals  of  which  is  impressed  an  E.M.F.  of  110  volts,  giving 
rise  to  a  current  of  \  ampere  which  flows  for  2  hours.  Find  the  heat  in 
calories. 

12.  Considering  the  data  of  exercise  11,  find  the  power  expended  on 
the  lamp  in  (a)  watts,  (b)  kilowatts. 

13.  Find  the  total  electrical  energy  expended  during  the  2  hours  in 
(a)  watt  hours;    (b)  kilowatt  hours. 

14.  Find  the  total  energy  expended  upon  the  lamp  (exercise  12)  in 
(a)  ergs;    (b)  joules  (Art.  100). 

15.  What  will  be  the  cost  of  running  this  lamp  for  2  hours  at  the  rate 
at  which  electrical  energy  is  sold  in  your  town  ? 


CHAPTER  IX 


ELECTROMAGNETIC  INDUCTION 

INDUCED  ELECTROMOTIVE  FORCE 

375.  Faraday's  Experiment.  Experiment.  If  a  magnet  be 
thrust  into  a  coil  of  wire  the  ends  of  which  are  connected  to  a 
galvanometer,  Fig.  326,  the  needle  will  be  deflected  in  a  given 
direction;  when  the  magnet  is  withdrawn  from  the  coil,  the 

needle  will  be  deflected  in 
the  opposite  direction. 
The  current  which  flows 
through  the  coil  and  gal- 
vanometer when  the  mag- 
net is  being  thrust  in  or' 
pulled  out  is  called  an  in- 
duced current,  and  the 
electromotive  force  devel- 
oped by  the  motion  of  the 
magnet  is  called  an  induced 
E.M.F. 

This  induced  electromo- 
tive force  and  resulting  in- 
duced current  is  caused  by  the  cutting  of  the  lines  of  magnetic 
induction  across  the  wires  of  the  coil.  If  a  magnet  be  thrust 
into  a  coil  and  held  stationary,  no  current  flows  so  long  as  the  mag- 
net is  at  rest.  The  induced  E.M.F.  manifests  itself  only  while 
the  magnet  is  in  motion ;  that  is,  while  there  occurs  an  increase 
or  decrease  of  the  lines  of  induction  threading  through  or  cut- 
ting across  the  coil.  It  is  important  to  note  that  an  induced 
current  flows  only  while  the  magnet  is  in  motion  and  the  coil 
is  closed.  If  the  coil  be  open  while  the  magnet  is  in  motion 


FIG.  326 


ELECTROMAGNETIC   INDUCTION  241 

there  will  occur  in  the  wire,  as  before,  an  induced  E.M.F., 
but  no  current.  Induced  currents  always  occur  as  a  result  of 
induced  electromotive  forces. 

This  experiment  was  first  performed  by  Faraday  in  1831.' 
The  relation  of  magnetism  to  electricity,  as  here  shown,  is 
known  as  the  phenomenon  of  electromagnetic  induction,  upon 
which  basis  nearly  all  modern  electrical  industries  have  been 
developed. 

376.  Relation  of  the  Lines  of  Induction  to  the  Induced 
E.M.F.  We  have  seen,  from  the  preceding  experiment,  that 
when  lines  of  magnetic  induction  cut  across  a  wire  there  is 
set  up  in  the  conductor  an  induced  E.M.F.  which,  if  the  con- 
ductor be  closed,  gives  rise  to  an  induced  current.  We  have 
also  learned  that  when  a  current  flows  through  a  conductor, 
lines  of  magnetic  induction  are  set  up  in  the  medium  around 
the  wire.  That  is,  currents  give  rise  to  magnetic  lines  of  induc- 
tion, and,  on  the  other  hand,  the  motion  of  magnetic  lines  of 
induction  may  give  rise  to  induced  electromotive  forces  and 
induced  currents.  It  is  important,  therefore,  to  know  the 
relation  which  exists  between  the  direction  of  motion  of  the 
lines  of  induction  and  the  direction  of  the  induced  E.M.F. 
There  are  two  rules  which  are  commonly  employed  to  deter- 
mine this  relation  as  follows: 

1.  For  the  case  of  a  circular  conductor  the  following  rule  is 
serviceable.  Consider  that  the  N-pole  of  a  magnet  is  thrust  into 
a  coil  of  wire,  Fig.  327,  and  that  the  observer  is  in  such  a  posi- 


FIG.  327 

tion  as  to  look  in  the  direction  of  the  lines  of  induction,  that 
is,  from  the  S-  to  the  N-pole,  at  the  instant  the  magnet  is  thrust 


242 


HIGH   SCHOOL  PHYSICS 


into  the  coil  or  withdrawn.  When  the  N-pole  is  thrust  into 
the  coil  there  is  an  increase  of  the  lines  of  induction  threading 
through  the  coil  which  gives  rise  to  an  indirect  induced  E.M.F. 
'as  shown  by  the  arrows  in  Fig.  327.  When  the  N-pole  is 
withdrawn  there  is  a  decrease  of  the  lines  of  induction  which 
give  rise  to  a  direct  induced  E.M.F.,  Fig.  328.  The  words 
direct  and  indirect  as  here  used  refer  to  the  motion  of  the 
hands  of  a  watch  or  clock.  Direct  means  clockwise ;  indirect, 
counter-clockwise.  This  rule  may  easily  be  remembered  if  it 
be  kept  in  mind  that  i  stands  for  increase  and  also  for 
indirect;  likewise  d  stands  for  decrease  and  also  for  direct. 

2.  A  second  rule  for  determining  the  direction  of  the  induced 
E.M.F.  is  as  follows:  Suppose  that  a  conductor  AB  move 
downward  through  a  magnetic  field,  Fig.  329,  cutting  across 
the  lines  of  induction.  The  direction  of  the  induced  E.M.F. 


FIG.  329 


FIG.  330 


in  the  conductor  is  from  A  to  B.  Each  line  on  being  cut  may 
be  conceived  of  as  tending  to  wrap  itself  around  the  conduc- 
tor, as  shown  in  Fig.  330.  Now  if  we  grasp  the  wire  with  the 
right  hand,  the  fingers  being  in  the  direction  of  the  lines  of 
induction  encircling  the  conductor,  the  thumb  will  indicate 
the  direction  of  the  induced  E.M.F.  It  will  be  noted  that 
this  is  nothing  more  than  the  application  of  the  right  hand 
rule  as  used  to  determine  the  deflection  of  a  magnetic  needle, 
as  explained  in  Art.  338.  This  right  hand  rule  is  of  great 
importance  because  of  its  wide  application  in  connection  with 
the  study  of  electromagnetic  apparatus. 

In  text-books  on  electricity  the   following  convention  has 


ELECTROMAGNETIC  INDUCTION 


243 


been  adopted  with  reference  to  the  direction  of  the  E.M.F. 
Looking  at  the  end  of  a  conductor,  a  cross,  representing  the 
feathered  end  of  an  arrow,  indicates  an  E.M.F.,  or  a  current 
flowing  away  from  the  observer,  that  is,  into  the  paper;  a  dot, 
representing  the  point  of  an  arrow,  indicates  an  E.M.F.  or  cur- 
rent directed  out  of  the  paper  and  toward  the  observer.  In 
Fig.  331  there  is  shown  the  relation  of  the  direction  of  the  lines 
of  induction  about  the  conductor  to  the  direction  of  the  induced 
E.M.F.,  in  one  case  in  and  the  other  out. 


EXERCISES:  1.  A  conductor  C,  Fig.  332,  moves  through  the  magnetic 
field  from  C  to  A.  Will  the  induced  E.M.F.  be  directed  toward  or  from 
the  observer;  that  is,  will  it  be  in  or  out? 

2.  What  will  be  the  direction  of  the  induced  E.M.F.  if  the  conductor 
of  Fig.  333  move  from  C  to  B  ? 

3.  Find  the  direction  of  the  induced  E.M.F.  when  the  conductor  C, 
Fig.  334,  moves  in  the  direction  (a)  C  to  A;    (b)  C  to  B',    (c)  C  to  F; 
(d)  Cto  G;  (e)  D  to  E. 


4 


F 


D -©--      - 


G 


FIG.  334 


C  -  B 

FIG.  335 


4.  Find  the  direction  of  the  induced  E.M.F.  when  the  conductor, 
Fig.  335,  moves  through  the  field  (a)  from  A  to  B;  (b)  C  to  D.  At  what 
two  points  does  the  direction  of  the  induced  E.M.F.  change? 


244  HIGH  SCHOOL  PHYSICS 

377.  Value  of  the  Induced  E.M.F.     The  electromotive  force 
induced  in  a  circuit  depends  upon  the  number  of  lines  cut  per 
unit  of  time.     Now  the  number  of  lines  cut  per  second  depends, 
in  turn,  upon  three  factors :  (a)  the  number  of  lines  in  the  field, 
(b)  the  number  of  conductors  cutting  the  lines,  and  (c)  the 
speed  at  which  the  cutting  occurs.     In  the  case  of  a  magnet 
thrust  into  a  coil,  the  number  of  lines  cut  per  second  will  depend 
upon  the  pole  strength  of  the  magnet,  the  rate  at  which  it  is 
moved,  and  the  number  of  turns  of  wire  in  the  coil.     It  is  there- 
fore evident  that  if  it  were   desired  to  design   an  apparatus 
which  would  give  a  maximum  induced  E.M.F.,  it  would  be 
necessary  to  provide  for  three  things:  first,  a  strong  magnetic 
field;   second,  the  use  of  as  many  turns  of  wire  in  the  coil  as 
would  be  practicable;   and  third,  as  high  a  rate  of  cutting  of 
the  lines  as  possible.     This  is  practically  the  problem  which 
presents  itself  in  the  designing  of  many  pieces  of  electromag- 
netic apparatus,  such  as  certain  types  of  dynamos. 

378.  Self-induction.     Consider  Fig.  336.     When  the  key  is 
closed  a  current  from  the  battery  begins  to  flow  around  the 

circuit.  This  gives  rise  to  lines 
of  induction  in  the  direction  A  to 
B.  Now  the  appearance  of  the 
lines  of  induction  in  the  coil  has 
336  the  same  effect  as  if  an  N-pole 

were  thrust  in  from  A  to  B,  which 

would  produce  an  induced  E.M.F.  the  direction  of  which  is 
counter  clockwise.  This  is  called  the  counter  or  the  back 
E.M.F.  of  self-induction;  it  opposes  the  applied  E.M.F. 
furnished  by  the  battery.  The  back  E.M.F.  lasts  as  long  as 
the  lines  of  induction  in  the  coil  continue  to  increase.  This 
explains  why  the  current  in  such  a  coil  rises  to  its  maxi- 
mum value  slowly;  it  is  due,  in  other  words,  to  the  counter 
E.M.F.  of  self-induction. 

In  a  like  manner,  when  the  key  is  opened  and  the  current 
broken,  the  lines  of  induction  drop  out  of  the  coil,  thus  having 


ELECTROMAGNETIC  INDUCTION  245 

the  same  effect  as  the  withdrawing  of  a  magnet.  This  again  pro- 
duces an  E.M.F.  of  self-induction  which  in  this  case  tends  to 
prolong  the  current  after  the  circuit  is  broken. 

Thus  it  is  seen  that,  when  a  current  flowing  through  a  coil 
is  changing  in  value,  that  is,  increasing  or  decreasing,  there  is 
present  in  the  coil  a  counter  E.M.F.  of  self-induction,  which 
tends  to  oppose  the  increase  of  the  current  at  the  instant  the 
circuit  is  closed,  and  which  likewise  tends  to  prolong  the  cur- 
rent after  the  circuit  is  broken. 

379.  Lenz's  Law.     This  opposition  to  change  in  an  electro- 
magnetic system  is  formulated  by  Lenz's  law,  which  may  be 
stated  as  follows:    When   a  change  takes 

place  in  an  electromagnetic  system,  that 
thing  happens  which  tends  to  oppose  the 
change.  Thus,  by  way  of  illustration,  if 
we  attempt  to  thrust  a  magnet  into  a 
coil,  Fig.  337,  there  is  developed  in  the 
coil,  due  to  the  induced  current,  poles 
which  oppose  the  motion  of  the  magnet; 
and  likewise  if  we  attempt  to  withdraw  a 
magnet  from  a  coil,  a  reverse  induced 
current  is  produced  which  in  turn  gives 
rise  to  a  magnetic  field  opposing  the  mo- 
tion of  the  magnet.  This  all  means  that  FIG.  337 
whenever  we  produce  any  change  in  the 
magnetic  system,  work  has  to  be  done  in  overcoming  the 
opposing  forces.  Lenz's  law  has  a  very  wide  application  in 
electromagnetics. 

THE  DYNAMO  AND  ITS  USE 

380.  The  Dynamo.     One  of  the  most  important  pieces  of 
electromagnetic  apparatus  is  the  dynamo,  a  machine  designed 
for  changing  mechanical  energy  into  electrical  energy,  or  for 
changing  electrical  energy  into  mechanical  energy.     When  a 
dynamo  is  used  for  the  purpose  of  transforming  mechanical 


246 


HIGH   SCHOOL  PHYSICS 


energy  into  electrical  energy  it  is  called  a  generator;  when  it 
is  used  to  transform  electrical  energy  into  mechanical  energy 
it  is  called  a  motor.  The  fundamental  principle  governing  the 
operation  of  the  dynamo  used  as  a  generator  is  the  production 
of  an  induced  E.M.F.  by  the  cutting  of 
lines  of  induction;  and  when  used  as  a 
motor,  the  production  of  mechanical  mo- 
tion due  to  the  reaction  of  two  magnetic 
fields. 

381.  The  Simple  Dynamo.  Let  us  con- 
sider the  dynamo  as  a  generator.  One  of 
the  simplest  forms  of  generators  is  that 
illustrated  in  Fig.  338.  When  the  mag- 
net is  thrust  into  the  coil,  lines  of  induc- 
tion cut  across  the  wires  of  the  armature 
and  a  momentary  current  flows  through 
the  circuit;  when  the  magnet  is  with- 
drawn the  lines  of  induction  cut  across 
the  conductors  in  the  opposite  direction 
and  a  momentary  current  flows  through 
the  circuit  in  the  opposite 
direction.  Such  a  simple  dy- 
namo would  give  an  alternat- 
ing current;  that  is,  a  current 
flowing  at  one  instant  around 
the  circuit  in  one  direction 
and  at  the  next  instant  in 
the  opposite  direction. 

In  the  commercial  dynamo, 
however,  the  cutting  of  the 
lines  of  induction  may  be  ac-  FIG 

complished  not  by  moving 
the  magnet,  but  by  moving  the  coil  or  armature;  that  is,  by 
the  rotation  of  the  armature  about  its  axis  in  the  magnetic 
field,  as  shown  in  Fig.  339.  When  the  armature  rotates 


FIG.  338 


ELECTROMAGNETIC   INDUCTION 


247 


through  the  arc  abc,  that  is,  makes  one  half  revolution,  the  cut- 
ting of  the  lines  of  induction  gives  rise  to  an  induced  E.M.F. 
as  indicated  by  the  arrows;  on  the  second  half  of  the  revo- 
lution, that  is  cda,  the  cutting  of  the  lines  of  induction  is 
reversed  with  respect  to  the  conductors  and  the  induced 
E.M.F.  is  in  the  opposite  direction.  Thus,  starting  with  the 
armature  coil  in  a  vertical  position,  ac,  the  current,  for  the  first 
half  revolution,  flows  around  the  coil  in  one  direction;  for  the 
second  half  revolution,  in  the  opposite  direction.  The  current  in 
the  armature,  then,  is  always  an  alternating  current. 

382.  Terms  Relating  to  the  Dynamo.  The  magnets  repre- 
sented by  N  and  S,  Fig.  340,  are  called  the  field  magnets,  and 
the  space  between  them  is  called  the 
magnetic  field.  The  coil  of  wire 
which  rotates  in  this  field,  is  the 
armature.  The  two  metal  strips  B 
and  Bf,  which  conduct  the  current 
from  the  armature,  are  the  brushes. 
The  conductor  through  which  the 
current  flows  is  the  external  circuit, 
or  main  line. 

When  the  current  is  conducted  from  the  armature  to  the 
brushes  by  means  of  separate  rings,  Fig.  340,  one  attached  to 

N      each  end  of  the  wire  of  the 

\     armature,  the  dynamo  de- 
J    livers  to  the  main  line  an 
/'     alternating  current,  and  is 

for  this  reason  called   an 
FIG.  341 

alternating  current  dy- 
namo. The  symbol  for  the  term  alternating  current  is  A.C., 
and  the  diagram  which  is  commonly  employed  to  represent  an 
A.C.  dynamo  (generator  or  motor)  is  shown  in  Fig.  341. 

When  the  current  is  conveyed  to  the  brushes  by  metallic 
segments,  c  and  c',  Fig.  342,  which  device  is  called  a  com- 
mutator, the  dynamo  is  called  a  direct  current  dynamo.  The 


FIG.  340 
Alternating  Current  Dynamo 


248 


HIGH   SCHOOL  PHYSICS 


symbol  for  the  term  direct  current  is  D.C.,  and  the  diagram 
illustrative  of  the  D.C.  dynamo  is  that  of  Fig.  343.  A  graphic 
representation  of  an  end  view  of  a  commutator  and  brushes  is 
shown  in  Fig.  344. 


FIG  343 


FIG.  342 
Direct  Curreat  Dynamo 


FIG.  344 


383.  Graphic  Representation  of  an  Alternating  Current.  It 
is  sometimes  desirable  to  represent  graphically  currents  fur- 
nished by  A.C.  and  D.C.  generators.  An  alternating  current 
is  represented  by  the  curve  of  Fig.  345,  in  which  that  portion 


FIG.  345 


of  the  curve  above  the  line,  abc,  represents  the  current  flowing 
in  one  direction,  and  the  portion  below  the  line,  cde,  represents 
the  current  flowing  in  the  opposite  direction.  This  curve  also 
shows  the  rise  of  the  current  as  the  armature  rotates  through 
the  field.  When  the  armature  is  passing  through  the  position 
ac,  Fig.  339,  it  is  cutting  a  minimum  number  of  lines  of  induc- 
tion; hence  the  current  has  a  minimum  value,  as  represented  by 
the  points  a,  c,  and  e  on  the  curve.  When  the  armature  is  pass- 
ing through  the  position  bd,  Fig.  339,  it  is  cutting  a  maximum 
number  of  lines  of  induction ;  hence  the  current  is  a  maximum, 
as  represented  by  the  points  b  and  a. 

384.    Graphic    Representation    of    a    Direct    Current.     The 


ELECTROMAGNETIC   INDUCTION 


249 


curve  of  Fig.  346  represents  what  is  called  a  direct  current; 
that  is,  one  which  is  furnished  to  the  external  circuit  by 
the  use  of  a  commutator.  It  will  be  noted  that  all  the 
loops  of  the  curve  lie  on  one  side  of  the  axis.  This  means 
that  all  the  impulses  of  the  current  are  in  the  same  direc- 
tion. A  direct  current  as  furnished  by  a  generator  is  not 
necessarily  a  continuous  current,  but  rather  a  series  of  impulses. 


FIG.  346 

385.  The  Magnetic  Field  of  a  Dynamo.     In  general  dynamos 
depend  for  their  magnetic  induction  upon  the  principle  of  the 
electromagnet.     Indeed  the  poles  of  a  dynamo  are  in  reality 
nothing  more  than  the  poles  of   a  big  electromagnet.      The 
manner  of  exciting  this  magnet  depends  upon  the  use  to  which 
the  dynamo  is  put.     In  the  direct   current   generator  there  is 
usually  enough  residual  magnetism  in  the  poles  to  start  at  least 
a  small  current  in  the  armature  upon  its  rotation.     All  or  part 
of  this  current  is  caused  to  flow  around  the  field  circuit,  thus  in- 
creasing the  pole's  strength.  In 

this  way  the  dynamo  is  said  to 
"  build  up  "  its  magnetic  field. 
In   alternating   current    dy 
namos  this  method  of  exciting 
the    field    cannot    be   directly 
employed,    since    the    current 
in  the  external   circuit   is   an 
alternating   current.     In  A.C. 
generators,  therefore,  the  field  JPIG  347 

is  excited  from   some  outside 
source,  Fig.  347,  such  as  a  battery  or  a  small  D.C.  generator. 

386.  Kinds  of  D.C.  Generators.     With  reference  to  winding 
the  field  magnets  there  are  three  types  of  D.C.  generators, 
known  as  series,  shunt,  and  compound  wound. 


250 


HIGH  SCHOOL  PHYSICS 


In  the  series  wound  dynamo,  Fig.  348,  all  the  current  of  the 
main  circuit  passes  around  the  field  circuit.  In  the  shunt 
wound  dynamo,  Fig.  349,  only  a  portion  of  the  current  is 
carried  around  the  field  circuit.  In  the 
case  of  the  compound  wound  dynamo, 
Fig.  350,  there  is  a  double  circuit 
around  the  field  magnet,  consisting  of 
both  the  shunt  and  the  main  line. 
The  compound  wound  dynamo  is  very 
largely  employed  today  where  it  is 
desired  to  furnish  a  constant  E.M.F. 
at  some  distant  point  from  the  power 
house. 

A  discussion  of  the  theory  and  use  of 

theSG  three  tvP6S  is  bey°nd  the  limits 
of  an  elementary  text;  suffice  it  to  say 

that  in  general  the  series  machine  was  designed  to  furnish  cur- 
rents of  constant  strength;  shunt  and  compound  wound 
machines  to  furnish  currents  of  constant  potential. 


cttfc^T 

FIG.  348.— Series  Dynamo 


FIG.  349.  —  Shunt  Dynamo 


FIG.  350.  —  Compound  Dynao 


387.   The  Alternating  Current  Dynamo.     Generators  of  the 
A.C.  type  are  now  almost  universally  used  for  the  purpose  of 


ELECTROMAGNETIC   INDUCTION 


251 


commercial  lighting.  The  alternating  current  dynamo  differs 
in  •  principle  from  the  direct  current  dynamo,  as  already  ex- 
plained, in  only  two  respects:  (a)  The  armature  of  the  machine 
is  provided  with  rings  instead  of  a  commutator  and  (b)  the 
field  of  the  A.C.  generator  has  to  be  excited  by  some  outside 
source. 

388.  The  Electric  Motor.  An  electric  motor  is  a  device  for 
transforming  the  energy  of  an  electric  current  into  the  energy 
of  mechanical  motion.  The  principle  of  the  motor  does  not 
differ  from  that  of  the  generator,  except  that  in  one  case  the 
armature  is  rotated  by  mechanical  means,  thus  generating  a 
current ;  while  in  the  other  case  a  current  is  forced  through  the 
armature,  causing  it  to  rotate,  due  to  a  distortion  of  the  mag- 
netic field.  Any  ordinary  D.C.  generator,  if  connected  up 
with  a  source  of  E.M.F.,  will  operate  as  a  motor;  and  on  the 
other  hand,  any  D.C.  motor  may  be  operated  as  a  generator. 
For  example,  if  an  electric  car  be  allowed 
to  run  down  grade,  its  motor  may  act  as 
a  generator. 

Motors  are  of  two  general  types,  with 
respect  to  the  kind  of  current  they  are 

designed  to  take;  namely,  (a)  D.C. 
motors  and  (b)  A.C.  motors. 

389.  Direct  Current  Motors. 
A  D.C.  motor,  like  a  D.C.  gen- 
erator, is  provided  with  a  com- 
mutator. As  the  current  flows 
through  the  armature  wires,  lines 
of  induction  appear  around  each, 
Fig.  351,  thus  distorting  the  mag- 
netic field.  A  photograph  of  such 
a  distorted  field  is  shown  in  Fig.  352.  A  wire  was  passed 
through  two  holes  in  a  glass  plate,  in  at  A,  then  around  and 
out  at  B.  The  plate  was  then  placed  upon  the  poles,  N  and 
S,  of  a  magnet  and  iron  filings  sprinkled  upon  it.  When  no 


FIG.  351. 


FIG.  352 


252  HIGH  SCHOOL  PHYSICS 

current  flowed  through  the  wire  AB,  the  lines  of  induction 
passed  directly  from  N  to  S  in  straight  lines.  When,  however, 
a  current  was  passed  through  the  wire,  in  at  the  right  and 
out  at  the  left,  the  lines  of  induction  of  the  field  were  dis- 
torted. Now  the  tendency  of  these  distorted  magnetic  lines 
is  to  straighten,  thus  causing  the  armature  AB  to  rotate,  as 
shown  in  Fig.  351. 

390.  The  Back  E.M.F.  in  a  Motor.  Experiment.  When 
the  armature  of  a  motor  rotates  in  a  magnetic  field,  as  explained 
in  the  preceding  topic,  it  cuts  some  lines  of  induction  and  there- 
fore tends  to  act  as  a  generator.  This  gives  rise  to  a  counter 
or  back  E.M.F.  in  the  armature,  which  opposes  the  applied 
E.M.F.  at  the  brushes.  The  faster  a  motor  rotates,  therefore, 
the  greater  is  the  back  E.M.F.  developed,  and  hence  the  less 
current  it  takes.  This  fact  may  be  demonstrated  by  means  of  a 
motor,  in  the  circuit  of  which  there  is  connected  an  ammeter, 
Fig.  353.  When  the  current  is  turned  on,  the  pointer  of  the 


FIG.  353 

ammeter  gives  a  large  throw,  showing  that  a  large  current 
is  flowing  through  it.  As  the  motor  speeds  up,  however,  it 
develops  a  back  E.M.F.  which  opposes  the  applied  E.M.F. 
at  the  brushes  thus  cutting  down  the  current,  as  indicated 
by  the  fall  of  the  pointer. 

It  is  because  of  the  fact  that  the  current  through  the  arma- 
ture of  a  motor  depends  upon  its  speed  that  a  "  starting  box," 
Fig.  354,  is  used  in  connection  with  motors  of  any  considerable 
size.  A  starting  box  is  a  sort  of  resistance  box  so  devised  as 


ELECTROMAGNETIC   INDUCTION 


253 


FIG.  354.  —  Starting  Box 


to  enable  the  operator  by  throwing  a  switch  to  reduce  the 
resistance  in  the  circuit  and  thus  gradually  increase  the  E.M.F. 
as  the  motor  speeds  up.  If  the  full  current  were  turned 

on  while  the  motor  is  at  rest  the 

chances  are  that  the  initial  current     j  *  ti£j$   ~ 

would  be  so  great  that  the  armature 

would  be  burned  out.     The  motor-  // > 

mJUlb/    j^ 

man  on  the  trolley  cars  uses  a  form 
of  starting  box  which  he  operates 
in  starting  his  car. 

391.  The  Alternating  Current  Mo- 
tor.    Since  alternating  currents  are 
very  extensively  used  now  for  do- 
mestic and  public  lighting,  it  is  not 
always    convenient    or   possible    to 
make  use  of  the  D.C.  motor.     Alter- 
nating current  motors  are  therefore  commonly  employed.     Of 
the  A.C.  motors  there  are  a  number  of  different  types,  the  one 
in  most  common  use  being  known  as  the  induction  motor,  a 
familiar  example  of  which  is  seen  in  the  small  motor  used  to 
operate  electric  fans,  sewing  machines,  vacuum  cleaners,  and 
similar  household  devices. 

392.  The  Transformer.     A  transformer  is  a  device  for  chang- 
ing a  current  of  high  potential  to  one  of  low  potential,  or  changing 

a  current  of  low  potential  to  one  of  high 
potential.     The  principle  may  be  under- 
stood by  considering  Fig.  355.     Sup- 
FIG.  355  Pose  that  an  alternating  current  flow 

in  the  coil  marked  P,  called  the  pri- 
mary. The  effect  of  this  current  in  the  primary  will  be  to  mag- 
netize the  bar  B.  This  will  have  the  same  effect  as  thrusting 
the  magnet  into  the  coil  S,  called  the  secondary.  Let  us  sup- 
pose that  the  effect  on  the  secondary  is  the  same  as  if  an  N-pole 
had  been  thrust  into  it.  When  the  current  reverses  in  the  pri- 
mary the  polarity  of  the  magnet  is  changed;  for  example,  an 


254  HIGH  SCHOOL  PHYSICS 

N-pole  becomes  an  S-pole.  The  effect  of  this  change  of  polar- 
ity is  the  same  as  if  the  magnet  were  withdrawn,  reversed  with 
regard  to  its  pole,  and  again  thrust  into  the  coil.  Now  it  will 
be  remembered  that  thrusting  an  N-pole  into  a  coil  gives  rise 
to  a  direct  E.M.F.;  withdrawing  the  magnet  gives  rise  to  an 
indirect  E.M.F.  So,  too,  every  time  the  current  flows  one 
way  in  the  primary  there  is  induced  an  E.M.F.  in  one  direc- 
tion, and  every  time  the  current  reverses  in  the  primary  there 
is  induced  in  the  secondary  an  E.M.F.  in  the  opposite  direc- 
tion. An  alternating  current  in  the  primary  produces  an  alter- 
nating E.M.F.  in  the  secondary, 
and  therefore  an  alternating  current 
provided  the  secondary  circuit  be 
closed. 

In  Fig.  356  there  is  shown  a  form 
of  transformer  of  the  ring  type.     A 
FIG.  356  coil  of  wire  P  is  the  primary  and 

S  the  secondary.  The  relation  be- 
tween the  E.M.F.  of  the  primary  and  that  of  the  second- 
ary is  determined  by  the  relation  of  the  number  of  turns  of 
wire  in  the  primary  to  the  number  of  turns  in  the  second- 
ary. This  relation  may  be  expressed  as  follows: 

E.M.F.  of  P:  E.M.F.  of  S  =  No.  turns  primary :  No.  turns 
secondary. 

Example.  An  alternating  current  having  an  E.M.F.  of  2200 
volts  flows  in  the  primary  of  a  transformer  having  200  turns 
in  the  primary  coil  and  -10  in  the  secondary.  Find  the  E.M.F. 
of  the  current  in  the  secondary.  Solution:  2200:  x  =  200:  10; 
hence  x  =  110  volts. 

This  means  that  by  the  use  of  such  a  transformer  as  described 
in  this  example  a  high  tension  current  having  an  E.M.F.  of 
2200  volts  could  be  "  stepped  down  "  to  a  current  having  an 
E.M.F.  of  110  volts. 

393.  The  Use  of  the  Transformer.  The  transformer  makes 
possible  the  transmission  of  electrical  energy  in  the  form  of 


ELECTROMAGNETIC   INDUCTION  255 

high  potential  alternating  currents  from  a  central  power  plant 
to  points  where  the  energy  is  to  be  used.  By  means  of  the 
transformer  a  current  on  the  high  tension  wires  may  always 
be  stepped  down  to  a  current  of  low  potential.  Small  com- 
mercial transformers,  as  shown  in 
Fig.  357,  are  often  attached  to  elec- 
tric lighting  poles  adjacent  to  dwell- 
ings. Their  function  is  of  course  to 
step  the  high  potential  current  down 
to  one  of  low  potential  such  as  is 
safe  to  use  in  the  lighting  of  houses, 
the  running  of  domestic  motors,  etc. 

The  reason  for  using  high  ten- 
sion currents  on  the  transmission 
lines  is  primarily  one  of  economy  FIGL  357 

in  two  respects,     (a)  When  a  very 

high  E.M.F.  is  used  very  little  attention  has  to  be  paid  to 
the  resistance  of  the  line.  The  effect  of  high  resistance  can 
always  be  overcome  by  using  a  still  higher  E.M.F.  We 
may  therefore  use  relatively  fine  wire  for  the  high  transmis- 
sion purposes,  its  resistance  not  being  an  important  factor. 
The  use  of  fine  wires  means  a  reduction  in  the  expense  of  in- 
stalling the  system,  (b)  There  is  another  reason  also  why  a 
current  of  high  voltage  and  low  amperage  is  economical  so  far 
as  transmission  is  concerned,  and  that  is  the  fact  that  the  heat 
lost  for  low  current  transmission  is  very  much  less  than  that 
for  high  current,  since  the  heat  generated  in  a  conductor  is 
proportional  to  the  square  of  the  current  strength.  We  thus 
see  that  in  high  tension  transmission  we  use  wire  through 
which  there  flows  currents  of  low  amperage  but  of  very  high 
voltage.  By  means  of  transformers  this  high  voltage  current 
is  stepped  down  to  one  of  low  voltage  and  proportionally  high 
amperage. 

394.   The  Electric  Car.     An  electric  railway  system  in  gen- 
eral includes  a  D.C.  generator,  a  circuit,  including  the  trolley 


256  HIGH  SCHOOL  PHYSICS 

wires  and  tracks,  and  cars  provided  with  D.C.  motors,  Fig. 
358.  It  is  customary  to  generate  the  electric  power  at  some 
central  station  and  then  to  distribute  it  to  the  various  sub- 
stations by  means  of  high  tension  alternating  currents  under 

a    pressure,    usually    of 

. ^  Trolleu  Wire ,       ,    nn  „„„       ,, 

•  about  23,000  volts.     At 


the  transforming  station 
these  high  tension  cur- 
mmm .^^     rents  are  stepped  down 
FIG  355  by  means  of  transform- 

ers to  a  relatively  low 

voltage.  This  low  voltage  alternating  current  is  then  changed 
to  a  direct  current  by  means  of  a  device  known  as  a  rotary 
converter,  which  changes  the  alternating  current  form  the 
transformer  into  a  direct  current,  which  is  supplied  to  the 
trolley  wires.  The  potential  between  the  trolley  wire  and 
the  track  is  usually  about  650  volts. 

ELECTROMAGNETIC  APPLIANCES 

395.  The  Electric  Bell.     The  essential  parts  of  an  electric 
bell  system  are  the  battery,  the  push  button,  and  the  bell,  as 
shown  in  Fig.  359.     The  push  button,  Fig.  360,  is  a  device  for 
making  and  breaking  the  circuit.     The  parts  of  an  electric 
bell  are  shown  in  outline  in  Fig.  361.     When  the  circuit  is  closed 
by  pressing  the  button  the  current  from  the  battery  magnetizes 
the  iron  core  of  the  electromagnet  ra.     This  attracts  the  iron 
strip  a,  causing  a  break  in  the  circuit  at  s.     As  the  piece  of  iron 
moves  downward  it  causes  the  clapper  c  to  strike  the  bell. 
The  moment  the  circuit  is  broken,  however,  the  spring  throws 
the  armature  a  back  to  the  point  s,  thus  again  closing  the 
circuit. 

396.  The  Telegraph.     The  operation  of  telegraphing  from 
one  point  to  another  by  means  of  the  key  and  sounder  system 
may  be  explained  in  connection  with  Fig.  362.     The  current 
from  the  battery  at  station  A  may  be  traced  through  the  elec- 


ELECTROMAGNETIC   INDUCTION 


257 


tromagnet  m  through  the  line  L,  the  electromagnet  mf,  the 
battery  at  B,  thence  through  the  earth  back  to  A. 

Suppose  now  we  wish  to  telegraph  from  A  to  B.     The  oper- 
ator first  opens  his  switch  s.     He  now  presses  down  key  k, 


FIG.  359 


FIG.  360 

Push  Button 


FIG.   361 
Diagram  of  Electric  Bell 


which  closes  the  circuit  through  the  line  to  B  and  back  through 
the  earth.     When  the  current  passes  through  the  two  electro- 


FIG.  362.  —  Diagram  of  Simple  Telegraph 


magnets  m  and  m' ,  a  and  b  are  drawn  down,  giving  rise  to  the 
clicking  noise  characteristic  of  the  telegraph  instrument.     The 


258 


HIGH   SCHOOL  PHYSICS 


combination  of  magnet  and  armature  is  called  a  sounder. 
Every  time  the  key  at  A  is  pressed  down  there  is  produced 
in  the  sounder  at  both  A  and  B  corresponding  long  or  short 
clicks,  called  dots  and  dashes.  The  operator  at  B  reads  the 
dots  and  dashes  as  they  are  sounded  upon  his  instrument,  and 
writes  out  the  message.  When  the  operator  at  A  is  through 


FIG.  363.  —  Telegraph  Key 


FIG.  364.  —  Telegraph  Sounder 


sending,  he  closes  the  switch  s.  This  diagram  above  shows 
only  two  stations.  In  actual  practice  a  great  many  stations 
may  be  on  the  line.  The  essential  pieces  of  apparatus  in  each 
station,  however,  is  the  key>  Fig.  363,  and  the  sounder,  Fig. 
364.  When  the  line  is  a  long  one,  the  current  is  sometimes  too 


O  -  -  U 

p -y 

R X 

S Y 

T  —  Z 


A  

H 

B  —  -•-- 

I 

C  --    - 

J 

D  

K 

E  - 

L 

F  

M 

G  

N 

FIG.  365.  —  Morse  Alphabet 

weak  to  operate  the  sounder.  In  this  case  there  is  used  a  relay, 
which  is  an  electromagnet  devised  to  open  and  close  a  local 
circuit  which  is  strong  enough  to  operate  the  local  sounder. 
(Supplement,  579.) 

In  Fig.  365  there  is  shown  the  Morse   code,  in  which   dots 
and  dashes  represent  letters  of  the  alphabet. 


ELECTROMAGNETIC  INDUCTION 


259 


397.  The  Telephone.     The  characteristic  features  of  a  simple 
telephone  are  shown  in  Fig.  366.     The  working  parts  of  a 
telephone  system  as  outlined  in  Fig.  367  are  the  transmitter  T, 
the  receiver  R,  induction  coil  I,  local  battery  and  the  line  L. 

The  operation  of  the  system  may  be  briefly  explained  thus. 
When  a  person  speaks  into  the  transmitter  T,  Fig.  367,  the 
metallic  diaphragm  is  set  in  vibration, 
pressing  against  the  carbon  c,  and  thus 
producing  a  variable  resistance  in  the 
local  circuit.  This  varying  current  in 
the  induction  coil  I  produces  an  in- 
duced current  in  the  line  which  affects 
the  magnet  of  the  receiver  R',  the 
diaphragm  of  which  is  set  in  vibra- 
tion. It  is  the  vibrations  of  this  dia- 
phragm which  produce  the  characteristic 
tones  of  the  telephone.  When  a  per- 
son speaks  into  the  transmitter  T'  the 

same  transmission  of  vibrations  occur  with  respect  to  the 
receiver  R. 

398.  The  Induction  Coil.     An  induction  coil  is  an  apparatus 
for  producing  high  E.M.F.  by  the  principle  of  electromagnetic 
induction.     It  is  really  a  step-up  transformer.     The  appear- 


FIG.  366 


FIG.  367.  —  Diagram  of  Simple  Telephone 

ance  of  the  ordinary  coil  is  shown  in  Fig.  368;  a  sectional  draw- 
ing in  Fig.  369.     Surrounding  the  iron  core  are  two  coils  of  wire, 


260  HIGH  SCHOOL  PHYSICS 

the  primary  P  and  the  secondary  S.  The  primary  coil  which 
is  wrapped  directly  around  the  core  consists  of  a  few  turns  of 
heavy  insulated  wire,  which  is  connected  with  the  battery. 
The  secondary  wire  consists  of  many  turns  of  very  fine  wire, 
and  is  not  connected  in  any  way  with  the  primary.  Under- 
neath the  coil  is  a  condenser  C  which  consists  of  a  number  of 
sheets  of  tin  foil  carefully  insulated  from  each  other. 


FIG.  368.  —  Induction  Coil 

The  operation  of  the  coil  is  as  follows:  When  the  key  is 
closed  a  current  flows  around  the  primary  circuit,  thus  magnet- 
izing the  core,  which  in  turn  attracts  the  iron  a.  This  breaks 
the  primary  circuit  exactly  as  in  the  case  of  the  electric  bell. 
Now  the  effect  of  magnetizing  and  demagnetizing  the  core  is 
exactly  the  same  as  if  a  magnet  were  thrust  into  the  second- 
ary and  withdrawn  again,  thus  inducing  alternating  currents. 
Since  the  induced  E.M.F.  in  the  secondary  depends  upon  the 
number  of  lines  qf  induction  cut  per  second  and  the  number  of 
lines  in  turn  depend  upon  the  number  of  turns  of  wire  in  the 
secondary,  the  greater  the  number  of  turns  in  the  secondary 
the  greater  will  be  the  induced  E.M.F.  When  the  coil  is  in 
operation  the  hammer  flies  back  and  forth  making  and  break- 
ing the  primary  circuit,  thus  magnetizing  and  demagnetizing 
the  core.  This  produces  an  induced  E.M.F.  in  the  secondary 
which  manifests  itself  in  the  stream  of  sparks  across  the  ter- 
minals of  the  secondary.  The  induced  E.M.F.  of  the  second- 


ELECTROMAGNETIC   INDUCTION 


261 


ary  is  usually  determined  by  the  length  of  spark  which  the 
apparatus  will  give  in  dry  air  between  the  spherical  knobs  of 
the  secondary.  To  produce  a  spark  one  centimeter  in  length 
between  spheres  of  one  centimeter  in  diameter  requires  a  poten- 
tial of  about  25,000  volts.  Induction  coils  have  been  made 
which  are  capable  of  giving  a  spark  50  centimeters  in  length. 
To  do  this  would  require  a  difference  of  potential  between  the 


FIG.  369 

knobs  of  the  secondary  of  more  than  a  million  volts.  It  must 
be  borne  in  mind,  in  this  connection,  that  the  induction  coil 
does  not  enable  us  to  increase  the  energy  furnished  by  the 
primary  circuit.  While  the  E.M.F.  of  the  secondary  circuit  is 
very  high  the  current  is  proportionally  small.  Since  the  power 
of  a  current  is  equal  to  El  we  see  that  if  E  be  increased  /  must 
be  decreased. 

399.  The  Use  of  the  Condenser.  The  condenser  C,  Fig. 
369,  consists  of  a  series  of  layers  of  tin  foil  which  are  carefully 
insulated  from  each  other  and  which  are  connected  to  the  pri- 
mary circuit  on  each  side  of  the  contact  point  6.  The  con- 
denser may  be  said  to  have  three  uses  in  connection  with  an 
induction  coil,  as  follows:  (a)  It  prevents  sparking  at  the  point 
6.  When  the  current  flows  around  the  primary  circuit  and  the 
hammer  a  is  drawn  away  from  the  point  b  a  spark  is  produced. 
The  production  of  a  spark  at  this  point  is  detrimental  for  two 


262  HIGH   SCHOOL  PHYSICS 

reasons:  it  tends  to  burn  off  the  point,  and  in  the  second 
place  it  prevents  a  sudden  breaking  of  the  primary  current. 
Now  when  the  condenser  is  in  the  primary  circuit  the  en- 
ergy of  the  primary  current,  instead  of  being  expended  in  the 
formation  of  a  spark,  is  expended  in  charging  the  condenser, 
one  side  becoming  positively  charged,  the  other  negatively 
charged. 

(b)  Now  while  the  hammer  a  is  drawn  to  the  magnet  and  the 
primary  circuit  is  broken,  the  condenser,  which  an  instant  before 
was  charged,  now  discharges  itself  back  jbhrough  the  battery 
and  around  through  the  primary  coil.     This  discharge  from 
the  condenser  traverses  the  primary  coil  in  the  opposite  direc- 
tion to  that  which  the  current  flows  from  the  battery,  thus 
suddenly  cutting  out  the  lines  of  induction  in  the  core.     This 
action  of  the  condenser  thus  tends  to  demagnetize  the  core 
more  rapidly  than  would  otherwise  be  possible,  and  thereby 
increases  the  time  rate  of  the  cutting  of  lines  of  induction  by 
the  secondary,  thus  increasing  the  induced  E.M.F. 

(c)  The  third  important  function  of  the  condenser  grows  out 
of  this  sudden  interruption  of  the  spark  at  the  break.     The 
current  at  "make"  takes  a  fraction  of  a  second  to  grow  up 
to  its  maximum  value;   while  at  the  "break"  by  the  use  of 
the  condenser  the  cessation  is  almost  instantaneous.     Thus  the 
rate  of  cutting  of  the  magnetic  lines  of  induction  is  much  greater 
at  the  "break"  than  at  the  "make."     The  induced  E.M.F.  at 
the  make  lasts  longer  than  at  the  break,  but  is  feeble  and  does 
not  suffice  to  send  sparks  across  the  gap.     On  the  other  hand, 
the  induced  E.M.F.  at  the  break  manifests  itself  by  a  brilliant 
torrent  of  sparks  between  the  terminals  of  the  secondary.     Thus 
we  may  say  that  one  function  of  the  condenser  is  to  produce  a 
uni-directional  current  between  the '  knobs  of  the  secondary. 
This  is  important  in  certain  kinds  of  experimentation,  as,  for 
example,  with  X-ray  tubes. 


ELECTROMAGNETIC   INDUCTION  263 

HIGH  POTENTIAL  PHENOMENA 

400.  Experiments  with  High  Tension  Currents.     By  means 
of  an  induction  coil  or  other  kind  of  transformer  it  is  possible 
to  step  a  current  up  to  a  very  high  potential.     Now  when 
currents  of  high  potential  occur  in  the  form  of  a  spark  discharge 
some  very  beautiful,  interesting,  and  at  the  same  time  highly 
important  results  are  obtained.     A  few  years  ago  experiments 
with  high  tension  currents  were  considered  to  be  interesting 
but  of  little  practical  value.     Today,  however,  the  production 
of  the  Roentgen  or  X-rays,  the  operation  of  wireless  telegraphy, 
and  similar  phenomena  are  not  only  of  great  scientific  interest, 
but  also  of  immense  commercial  importance. 

401.  The   Geissler  Tube.    Geissler   tubes  are   glass   tubes 
which  have  been  exhausted  to  a  low  pressure  and  sealed.     Into 
the  ends  of  the  tubes  there  are  sealed  two  short  pieces  of  plati- 
num wire  which  serve  as  electrodes.    When  these  electrodes  are 
attached  to  the  poles  of  a  static  machine  or  to  the  terminals  of 
an  induction  coil  the  tube  becomes  brilliantly  lighted  with  colors 
which  vary  with  the  nature  of  the  gas  enclosed  and  with  the 
kind  of  glass  of  which  the 

tube  is  made.  When  the 
tube  contains  a  trace  of 
nitrogen  the  color  given  on  FIG  370 

discharge   is   violet;    hydro- 
gen, on  the  other  hand,  gives  red.     These  tubes  are  often 
drawn  into  fantastic  shapes,  Fig.  370,  which  much  enhance  the 
beauty  of  their  color  effects. 

Geissler  tubes  derive  their  name  from  Geissler,  a  German 
physicist  (1814-1879),  who  invented  a  type  of  the  mercury  air 
pump,  which  he  used  in  the  exhaustion  of  these  tubes.  Geissler 
tube  effects  are  obtained  when  the  pressure  is  reduced  to  about 
0.002  of  an  atmosphere. 

402.  The  Crookes'  Tube.     The  Crookes'  tube,  named  after 
Sir  William  Crookes,  who  was  one  of  the  first  to  work  with  it, 


264 


HIGH  SCHOOL  PHYSICS 


FIG.  371 


is  a  tube  from  which  the  air  has  been  thoroughly  exhausted. 
Fig.  371  shows  a  form  of  the  Crookes'  tube  much  used  in  phys- 
ical laboratories  at  the  present  time  to  illustrate  the  Crookes' 
tube  effects.  A  and  C  are  platinum  electrodes  sealed  into  the 

glass.  B  is  a  tube  leading  to 
the  air  pump.  A  is  connected 
with  the  positive  pole  of  the 
high  tension  apparatus,  C  to 
the  negative  pole;  A,  there- 
fore, is  the  anode  and  C  the  cathode.  Let  us  suppose,  to 
begin  with,  that  the  tube  is  filled  with  air.  On  turning  on 
the  current  no  spark  discharge  occurs  between  A  and  C. 
Now  if  the  tube  be  exhausted,  after  a  time  a  discharge  will 
occur  between  the  anode  and  the  cathode.  First 
it  occurs  as  a  reddish  band,  and  later,  as  the  ex- 
haustion continues,  this  breaks  up  and  the  tube 
glows  with  a  greenish  light.  When  this  occurs 
the  exhaustion  has  reached  the  point  of  about 
0.01  mm.  of  mercury.  The  tube  is  now  called 
a  Crookes'  tube,  and  a  regular  discharge  takes 
place  between  the  electrodes.  This  occurs  only 
when  the  exhaustion  has  been  carried  nearly  to 
the  point  of  a  perfect  vacuum. 

Another  familiar  form  of  the  Crookes'  tube  is 
that  shown  in  Fig.  372. 

403.  Cathode  Rays  and  Electrons.  Cathode 
rays  are  streams  of  particles  called  electrons  which 
are  shot  off  from  the  cathode  with  great  velocity, 
and  which  upon  striking  the  inner  portions  of  the 
tube  give  rise  to  the  characteristic  glow  already 
noted.  An  electron  is  a  particle  having  a 
of  electricity;  its  velocity  is  about  one-third  the  velocity  of  light. 
If  a  body  positively  charged  be  brought  near  a  stream  of 
electrons  they  are  attracted;  if  a  negative  body  be  presented 
they  are  repelled.  If  a  magnet  be  brought  near  them  as 


FIG.  372 

Crookes' 

Tube 


charge 


ELECTROMAGNETIC   INDUCTION 


265 


shown  in  Fig.  373,  the  cathode  rays  are  deflected  from  their 
course. 


FIG.  373.  —  Cathode  Rays  deflected  by  Magnet 

404.  The  X-Ray.      Roentgen  or  X-rays,  as  they  are  some- 
times called,  were  discovered  by  Roentgen,  a  German  physicist, 
in  1895.    The  exact  nature  of  these  rays  is  not  yet  perfectly  un- 
derstood.    Most  physicists  hold,  however,  that  they  are  pulses 
in  the  ether,  propagated  with  enormous  speed  through  space. 

It  is  important  to  note  that  the  X-ray  is  not  a  cathode  ray. 
When  cathode  rays  (streams 
of  electrons)  fall  upon  an  ob- 
ject, as  the  metal  reflector  of 
a  Crookes'  tube,  Fig.  374,  they 
give  rise  to  X-rays,  somewhat 
analogous  to  the  manner  in 
which  a  stone  dropped  into 
water  gives  rise  'to  water 
xwaves.  The  cathode  ray  is 
no  more  the  X-ray  than  the 
stone  is  the  water  wave;  one  is  the  cause  of  the  other.  X-rays 
do  not  carry  electrical  charges  and  cannot  be  reflected  or  re- 
fracted as  are  light  waves. 

405.  Properties    of    X-Rays.     Roentgen    rays  possess   cer- 
tain  remarkable   properties   which   may  be  stated    briefly  as 
follows:    (a)  Roentgen  rays  excite  phosphorescence  in  a  large 
number  of  substances,     (b)  Gases  through  which  Roentgen 
rays  pass  become  conductors  of  electricity.     Thus  if  a  charged 
electroscope  be  placed  in  the  neighborhood  of  an  active  X-ray 
tube  it  will  be  observed  that  the  gold  leaves  collapse,  the  charge 
of  the  instrument  being  rapidly  carried  away  by  the  conduct- 


FIG.  374.  — X-Rays 


266 


HIGH  SCHOOL  PHYSICS 


ing  air.  (c)  These  rays  have  great  penetrating  power,  being 
able  to  pass  through  bodies  of  considerable  thickness.  Differ- 
ent substances  absorb  the  rays  in  different  degrees,  as  is  well 
illustrated  by  the  parts  of  the  human  body.  The  bones,  for 
example,  absorb  the  rays  more  strongly  than  do  the  fleshy 
parts.  Metals  also  absorb  the  X-rays  more  strongly  than  do 
the  non-metals,  such  as  wood  or  paper.  The  penetrating  power 
of  Roentgen  rays  is  determined  largely  by  the  pressure  of  the 
gas  within  the  tube.  High  exhaustion  gives  rays  of  high  pene- 
trating power,  known  as  "  hard  rays  ";  somewhat  lower  ex- 
haustion gives  rays  of  less  penetrating  power  which  are  known 
as  "  soft  rays." 

Roentgen  rays  produce  photographic  action  somewhat  sim- 
ilar to  that  due  to  light,  giving  rise  to  the  X-ray  photograph  or 
radiograph. 

406.  The  Radiograph.  The  so-called  X-ray  photograph  is 
really  a  shadow  picture  cast  upon  the  photographic  plate  by  the 


FIG.  375.  —  Radiograph 


ELECTROMAGNETIC   INDUCTION 


267 


body  through  which  the  X-rays  are  passed.  The  possibility  of 
obtaining  these  radiographs  depends  upon  the  absorbing  power 
of  different  parts  of  the  body  to  be  photographed.  The  denser 
portions  of  the  human  body,  for  example,  such  as  the  bones, 
absorb  the  rays,  thus  giving  a  dark  impression  upon  the  pic- 
ture. In  Fig.  375  there  is  shown  a  radiograph  of  a  foot  en- 
closed within  a  heavy  shoe,  the  bones  of  the  foot  and  the  iron 
nails  of  the  shoe  standing  out  very  clearly. 

407.   The  Fluoroscope.     A  fluoroscope  is  an  apparatus  which 
enables  us  to  study  the  effects  of  X-rays  without  the  use  of 
photographic  plates.     It  consists  of  a 
box  as   shown   in   Fig.  376,  the  small 
end  of  which  is  so  constructed  as  to 
fit  closely  around  the  eyes.     Over  the 
large  end  is  placed  a  fluorescent  screen, 
made  usually  of  platino-barium-cyan- 
ide.      If  an  object,  such  as  the  hand, 
be  placed  between  this  screen  and  an    FlG-376-- 
X-ray  tube  the  outlines  of  the  denser  portions  of  the  body 
may  be  distinctly  seen.     Sometimes  the  fluoroscope  is  used 


FIG.  377.  —  Sealed  Package  and  Contents,  as  revealed  by  the 
Fluoroscope 


268  HIGH  SCHOOL  PHYSICS 

by  custom  house  officers  to  determine  the  contents  of  trav- 
elers' baggage.  Fig.  377  shows  a  sealed  package  and  also 
what  the  fluoroscope  revealed  as  to  the  nature  of  its  contents. 

408.  Electric  Waves.     In  1887  Hertz  (1857-1894),  a  German 
physicist,  discovered  that  electrical  oscillations,  such  as  occur 
on  the  discharge  of  a  Leyden  jar,  give  rise  to  electrical  waves  in 
the  ether.     Thus  when  the  oscillatory  discharge  occurs  between 
the  knobs  of  an  electric  machine  or  between  the  terminals  of 
an  induction  coil,  electric  waves  are  set  up  in  the  ether  and 
travel  out  in  all  directions  from  the  source. 

These  waves  are  capable  of  being  reflected,  refracted,  and 
polarized  the  same  as  light  waves;  in  fact  the  electric  waves 
seem  to  possess  all  the  properties  of  light  waves,  differing  only 
in  the  fact  that  they  are  very  much  longer  than  those  of 
light. 

409.  The  Principle   of   Wireless  Telegraphy.     In  order  to 
detect  waves,  Hertz  used  a  device  called  a  spark-gap  detector, 

Fig.  378.  This  consists  of  a  rectangu- 
lar wire  C  set  up  near  the  poles  of  an 
electric  machine  or  induction  coil.  It 
was  found  that  the  size  of  the  loop 
could  be  so  adjusted  that  when  a  spark 
passed  between  AB  a  smaller  spark 
would  appear  at  ab.  That  is  to  say, 
electric  disturbances  started  at  AB 
could  be  made  to  record  their  presence 
FIG.  378  at  ob.  When  the  loop  is  in  condition  to 

give  a  spark  at  the  knobs  ab,  it  is  said  to 

be  in  tune  with  the  discharging  system  AB.  This  discovery 
by  Hertz  contained  the  fundamental  principle  of  signaling 
through  space  by  means  of  electric  waves.  The  idea  of  the 
transmission  of  messages  by  means  of  electrical  waves  was 
later  developed  and  perfected  by  Marconi,  who  invented  the 
modern  wireless  system  which  in  recent  years  has  become  of 
such  great  commercial  importance.  (Supplement,  580.) 


a  b 


ELECTROMAGNETIC   INDUCTION  269 

EXERCISES  AND   PROBLEMS  FOR  REVIEW 

1.  What  is  the   distinction  between   a  magnetic   substance  and  a 
magnet? 

2.  State  the  law  of  magnetic  attraction  and  repulsion. 

3.  Explain  the  term  "  lines  of  induction."     These  lines  are  represented 
as  coming  out  of  which  pole  of  a  magnet?     Entering  which  pole? 

4.  A  magnetic  needle  placed  in  a  magnetic  field  always  tends  to  set 
itself  in  what  position  with  respect  to  the  lines  of  induction  of  the  field? 

5.  Make  drawings  to  illustrate  magnetic  field  between  (a)  like  poles; 

(b)  unlike  poles. 

6.  What  is  magnetic  induction?     Make  drawing  to  illustrate  the 
induction  which  occurs  in  a  piece  of  soft  iron  when  it  is  brought  near  a 
magnet.     Indicate  the  N-pole. 

7.  Explain  magnetic  dip.     Where  with  respect  to  the  earth  is  the  angle 
of  dip  90°  ? 

8.  Explain  angle  of  declination.     How  may  this  angle  be  determined 
for  a  given  place? 

9.  What  is  the  line  of  no  declination?     If  a  person  is  east  of  this  line 
how  will  the  magnetic  needle  point  with  reference  to  the  north  geographic 
pole?     What  is  "true  north"  from  a  given  place? 

10.  What  charge  is  developed  upon  glass  when  it  is  electrified  by 
rubbing  with  silk?     What  charge  on  sealing  wax  when  rubbed  with  flannel 
or  cat's  fur? 

11.  A  glass  rod  positively  electrified  is  brought  near  a  spherical  con- 
ductor.    Show  by  drawing  what  happens  on  the  conductor.     When  the 
charging  body  (glass  rod)  is  removed,  what  happens  to  the  two  charges 
on  the  conductor? 

12.  Explain  how  to  charge  an  electroscope  (a)  by  conduction;    (b)  by 
induction. 

13.  Make  drawings  to  illustrate  distribution  of  electricity  on  (a)  a 
sphere;    (b)  a  pointed  body.     Explain  the  action  of  points  in  discharging 
a  body.     Why  does  an  electrified  body  when  it  is  covered  with  dust  soon 
lose  its  charge? 

14.  Make  drawing  of  a  simple  voltaic  cell,  and  in  connection  with  this 
drawing  point  out  and  define  (a)  positive  electrode;  (b)  negative  electrode; 

(c)  electrolyte;    (d)  external  circuit;    (e)  internal  circuit. 

15.  What  is  electromotive  force?     To  what  is  it  sometimes  likened? 
Is  it  a  force?     In  what  units  is  it  measured? 

16.  On  what  does  the  electromotive  force  of  a  battery  depend?     What 
is  the  relation  of  the  size  of  a  battery  (a)  to  its  E.M.F.?    (b)  to  the  amount 
of  electrical  energy  which  it  can  furnish? 


270  HIGH  SCHOOL  PHYSICS 

17.  Define  local  action,  and  explain  how  it  may  be  remedied. 

18.  Define  polarization,  and  explain  how  it  may  be  remedied. 

19.  What  is  the  E.M.F.  of  (a)  a  gravity  cell?  (b)  Leclanche  cell?  (c) 
dry  cell?     Which  cell  would  you  use  on  open  circuit  work,  and  which  on 
closed  circuit  work,  and  why? 

20.  What  is  electrolytic  dissociation?     What  is  an  ion?     Write  equa- 
tions to  illustrate  the  dissociation  of  (a)  hydrochloric  acid;  (b)  sulphuric 
acid;  (c)  copper  sulphate. 

21.  Explain  briefly  the  decomposition  of  water  by  electrolysis.     What 
gas  appears  at  (a)  the  anode?  (b)  the  cathode?     What  are  the  relative 
volumes  of  hydrogen  and  oxygen? 

__    22.   State  Faraday's  law  of  electrolysis. 

23.  A  current  of  one  ampere  will  deposit  by  electrolysis  0.001118  gram 
of  silver  in  one  second.     What  current  will  be  required  to  deposit  100 
grams  of  silver  in  2  hours? 

24.  A  current  of  one  ampere  flows  through  two  electrolytic  cells  in 
series,  one  containing  silver  nitrate  (AgNOs)  and  the  other  copper  sulphate 
(CuSO4).     (a)  How  much  silver  will  be  deposited  in  1  hour?    (b)  How 
much  copper? 

25.  Make  drawing  to  illustrate  the  silver  coulometer  and  explain  its 
use  in  determining  current  strength. 

26.  Define:   Ampere,  ohm,  volt,  coulomb. 

27.  A  wire  which  is  stretched  in  a  north-south  direction  carries  a  cur- 
rent.    It  is  desired  to  find  the  direction  of  the  current,  and  to  this  end  a 
magnetic  needle  is  placed  below  the  wire.     The  N-pole  of  the  needle  is 
deflected  to  the  east.     Determine  by  the  right  hand  rule  the  direction  of 
the  current  in  the  wire.     On  another  occasion  the  needle  was  placed  above 
the  wire,  the  N-pole  being  again  deflected  to  the  east.     Find  the  direction 
of  the  current. 

28.  Wrap  a  string  around  a  lead  pencil  after  the  manner  of  a  solenoid. 
Consider  the  current  to  flow  in  a  given  direction  in  the  string,  and  deter- 
mine by  the  right  hand  rule  the  polarity  of  the  point  of  the  pencil. 

29.  State  Ohm's  law;  write  the  law  in  the  form  of  an  equation. 

30.  On  what  four  factors  does  the  resistance  of  a  conductor  depend? 
State  the  laws  of  resistance  in  the  form  of  an  equation. 

31.  Find  the  resistance  of  10  ft.  of  No.  30  platinum  wire,  the  value  for 
k  for  platinum  being  70  ohms  per  mil-foot.     The  diameter  of  a  No.  30 
wire  is  0.01003  in.,  that  is,  10.03  mils. 

32.  Find  the  resistance  of  1000  ft.  of  No.  18  iron  wire.     To  find  the 
value  of  k  for  iron,  see  Art.  350;  to  find  the  diameter  of  No.  18  wire,  see 
Supplement,  611. 

33.  A  conductor  consists  of  three  wires  connected  in  series,  the  resist- 


ELECTROMAGNETIC   INDUCTION  271 

ance  of  the  wires  being  10,  20,  and  30  ohms  respectively.     What  is  the 
resistance  of  the  conductor? 

34.  A  current  of  2  amperes  flows  through  the  conductor  of  problem 
33.    Find  (a)  the  fall  of  potential  (E  =  RI)  over  each  of  the  three  wires; 
(b)  the  fall  of  potential  over  the  entire  conductor. 

35.  Two  wires  of  20  and  30  ohms  resistance  are  connected  in  parallel 
between  the  points  A  and  B.     Find  the  resistance  of  the  two  wires  thus 
connected. 

36.  A  current  flows  through  the  two  wires  of  problem  35,  between  the 
points  A  and  B.     The  portion  of  the  current  flowing  through  the  first  wire 
(20  ohms)  is  3  amperes;    that  through  the  second,  2  amperes.     What  is 
the  fall  of  potential  over  (a)  the  first  wire?    (b)  the  second  wire? 

37.  A  current  of  11  amperes  flows  from  A  to  B  over  a  divided  circuit 
consisting  of  three  wires  in  parallel.     The  resistance  of  the  wires  is  10, 
20,  and  30  ohms  respectively.     Find  (a)  the  total  resistance  between  A 
and  5;  (b)  the  fall  of  potential  between  A  andB;  (c)  the  current  in  each 
wire. 

38.  It  is  desired  to  find  the  resistance  of  a  given  conductor,  AB,  by 
Ohm's  law.     A  current  is  passed  through  the  conductor.     An  ammeter 
placed  in  the  circuit  reads  2  amperes.     A  voltmeter  connected  to  the 
terminals  A  and  B  indicates  a  fall  of  potential  of  3  volts.     Find  the  resist- 
ance between  A  and  B. 

39.  Five  gravity  cells,  each  having  an  E.M.F.  of  1  volt  and  an  internal 
resistance  of  5  ohms,  are  joined  in  series.     A  wire  having  a  resistance  of 
25  ohms  is  connected  to  the  terminals  of  the  battery.     Find  (a)  the  resist- 
ance of  the  entire  circuit;    (b)  the  current  flowing  in  the  wire. 

40.  Suppose  that  the  5  cells  of  problem  39  are  connected  in  parallel. 
What  current  will  flow  through  the  wire? 

41.  The  E.M.F.  of  a  battery  is  equal  to  the  fall  of  potential  around  the 
entire  circuit.     A  wire  having  a  resistance  of  2  ohms  is  connected  to  the 
terminals  of  a  cell  having  an  internal  resistance  of  ,1  ohm.     The  current 
flowing  through  the  circuit  is  0.5  ampere.     Find  (a)  the  fall  of  potential 
over  the  external  circuit;    (b)  over  the  internal  circuit;    (c)  around  the 
entire  circuit.     WTiat  is  the  E.M.F.  of  the  cell? 

42.  Three  dry  cells,  each  having  an  E.M.F.  of  1.5  volts  and  an  internal 
resistance  of  1  ohm,  are  connected  in  series  to  a  conductor  having  a  resist- 
ance of  7  ohms.     Find  (a)  the  resistance  of  the  entire  circuit;    (b)  the  cur- 
rent in  the  conductor;   (c)  the  fall  of  potential  over  the  conductor;   (d)  the 
fall  of  potential  over  the  internal  circuit;    (e)  the  total  fall  of  potential 
around  the  entire  circuit.     How  does  this  total  fall  of  potential  compare 
with  the  E.M.F.  of  the  battery? 

43.  A  current  of  3  amperes  flows  for  10  minutes  through  a  wire  having 


272  HIGH  SCHOOL  PHYSICS 

a  resistance  of  5  ohms.     Find  the  amount  of  heat  generated  in  the  wire 
in  calories. 

44.  An  electric  flatiron  having  a  resistance  of  22  ohms  is  connected  to 
a  lamp  socket  which  gives  an  electric  pressure  of  110  volts.     Find  (a)  the 
current  flowing  through  the  flatiron;    (b)  the  amount  of  heat  in  calories 
generated  in  1  hour. 

45.  Find  the  power  expended  in  the  iron  in  (a)  watts;   (b)  kilowatts. 

46.  Find  the  energy  expended  in  kilowatt  hours  during  a  period  of  2 
hours  use.     Compute  the  cost  of  running  this  flatiron  at  the  rate  at  which 
electrical  energy  is  sold  in  your  town. 

47.  The  lines  of  induction  of  a  magnetic  field  are  directed  from  south 
to  north.     A  conductor  lying  in  an  east-west  direction  falls  vertically 
through  the  field.     Determine  by  the  right  hand  rule  the  direction  of  the 
induced  E.M.F. 

48.  A  single  armature  loop  makes  1  revolution  in  the  magnetic  field 
of  a  dynamo.     Explain  by  the  right  hand  rule  the  direction  and  changes 
of  the  induced  E.M.F.  during  this  revolution. 

49.  In  a  given  transformer  the  number  of  turns  in  the  primary  are  to 
those  in  the  secondary  as  10  :  1.     Is  this  a  step-up  or  a  step-down  trans- 
former?    An  E.M.F.  of  1000  volts  applied  to  the  primary  will  give  rise 
to  what  E.M.F.  in  the  secondary? 

60.   Make  outline  drawing,  and   explain  operation  of  (a)  an  electric 
bell;  (b)  simple  telegraph;  (c)  telephone;  (d)  induction  coil. 

For  additional  Problems  and  Exercises,  see   Supplement, 
580. 


CHAPTER  X 
SOUND 

SOUND  AND  WAVE  MOTION 

410.  Definition  of  Sound.     The  word  sound  is  used  in  two 
distinct   senses.       From   the   viewpoint   of  the   physiologist, 
sound  is  a  sensation;   from  that  of  the  physicist,  sound  is  that 
form  of  vibratory  motion  which  may  be  perceived  by  the  ear.     The 
question  is  often  asked :  If  a  tree  were  to  fall  and  there  were  no 
ear  to  hear,  would  there  be  any  sound?     In  the  sense  in  which 
the  word  is  used  in  physiology,  there  would  be  no  sound;   in 
the  sense  in  which  the  term  is  used  in  physics,  there  would  be 
sound,  because  the  tree  in  falling  would  set  up  vibrations  of  the 
air  which  would  be  capable  of  affecting  the  ear,  if  one  were 
present. 

Acoustics  is  that  branch  of  physics  which  is  devoted  to  the  study 
of  sound  and  its  properties. 

411.  The  Origin  of  Sound.     Experiment.     All  sound  origi- 
nates in  vibrating  bodies.      If  a  sound  be  traced  to  its  source, 
there  will  always  be  found  a  vibrating  body.     If  a 

tuning  fork  be  set  in  vibration  and  then  brought 

in  contact  with  a  small  glass  or  ivory  ball,  Fig.  379, 

the  ball  will  be  thrown  vigorously  from  the  fork, 

due  to  the  vibrations  of  the  latter.     Again,  if  the 

prongs  of  a  tuning  fork  be  thrust  into  water  the 

latter  will  be  thrown  about  in  a  fine  spray.     Other 

illustrations  of  the  fact  that  sound  is  generated  in 

vibrating  bodies  may  be  seen  in  the  vibration  of 

a  guitar  string.     If  the  string  be  plucked  aside  and     F 

released  it  will  give  a  musical  note,  and  at  the  same 

time  seem  to  spread  out  into  a  broad  band  with  a  hazy  outline, 


274  HIGH  SCHOOL  PHYSICS 

Fig.  380,  which  diminishes  to  the  original  size  of  the  string  as 
the  sound  dies  away.     Also  the  tremulous  motion  of  a  bell  may 

be  perceived  by  placing  the  hand 
upon  it  while  it  is  sounding. 
FlG  38Q  412.    Examples     of     Vibrations. 

It  has  been  stated  that  all  sound 

originates  in  vibrating  bodies.  Now  bodies  may  vibrate  in  a 
great  many  different  ways;  for  example,  the  branches  of  a  tree 
or  the  heads  of  grain  in  a  field  vibrate  back 
and  forth  in  the  wind,  each  part  in  its  mo- 
tion to  and  fro  traveling  through  the  arc  of 
a  circle.  Also,  a  ball  suspended  as  shown 
in  Fig.  381  is  an  example  of  a  to  and  fro 
vibration  in  which  the  body  during  each 
swing  sweeps  out  the  arc  of  a  circle.  A  chip 
on  the  surface  of  deep  water  moves  up  and 
down  when  a  wave  runs  under  it.  If  the  water  be 
shallow,  the  chip  not  only  moves  up  and  down,  but 
back  and  forth  as  well,  its  motion  being  elliptical. 

If  a  ball  attached  to  a  rubber  band  be  pulled 
downward  and  then  released  it  will  vibrate  up  and 
down    in   a   straight    line,    Fig.  382.     A  vibration 
somewhat    similar   to    this  occurs   when  a 
glass  rod  is  stroked  with  a  damp  cloth,  as 
shown  in  Fig.  383.     Grasp  the  rod  in  the 
middle  with  one  hand  and   with   a   damp 
cloth    stroke    one   end   lightly.     The   glass 
rod  will  emit  a  distinct  musical  note,  and 
at  the  same  time  a  tremulous  motion  will 
(j>      be  felt  by  the  hand  grasping  it.     Vibrations 
run  from  one  end  of  the  rod   to  the   other 
^      in   a   manner  somewhat   analogous  to  the 

•i?     oco  UP  and  down  motion  of  the  ball  attached 
riG.  ooZi 

to  the  rubber  band. 
413.    Wave   Motion.     When  a  disturbance  occurs   FIG.  383 


SOUND 


275 


in  an  elastic  medium,  suchfas  air  or  water,  waves  are  set  up. 
A  wave  motion  represents  a  continuous  handing  on  from  par- 
ticle to  particle  of  a  disturbance  in  a  medium  without  an 
actual  transfer  of  the  medium  itself.  One  of  the  most  familiar 


FIG.  384 

examples  of  wave  motion  is  that  which  occurs  on  the  surface 
of  water.  Suppose  that  a  stone  be  dropped  into  a  lake  or  a 
pond,  Fig.  384;  the  waves  run  out  from  the  point  of  disturb- 
ance in  concentric  rings.  To  the  observer  it  would  appear 
that  the  water  is  actually  being  carried  forward.  This  is  not 
true,  however,  as  may  be  seen  by  watching  the  motion  of  a 
chip  floating  upon  the  surface.  As  the  waves  move  forward 
from  A  to  B,  Fig.  385,  the  motion 
of  the  particle  upon  the  surface  is 
up  and  down,  as  from  c  to  d.  An- 
other excellent  illustration  of  wave 
motion  is  seen  in  the  passage  of  a  wind  wave  over  a  field  of 
grain.  As  the  wave  runs  forward  each  individual  head  of 
grain  swings  back  and  forth. 

The  distinction  between  the  motion  of  a  particle  of  the  medium 
and  the  motion  of  the  wave  itself  is  of  fundamental  importance. 
The  bobbing  up  and  down  of  the  chip  on  the  surface  of  the 
water  and  the  swinging  back  and  forth  of  the  head  of  grain  are 
both  illustrations  of  the  motion  of  the  particle  of  the  medium. 
In  the  case  of  the  water  the  motion  of  the  particle  (the  chip) 


276  HIGH  SCHOOL  PHYSICS 

is  at  right  angles  to  the  direction  j)f  the  motion  of  the  waves; 
in  the  case  of  the  grain  the  motion  of  the  particle  (head  of  grain) 
is  back  and  forth  in  the  same  general  direction  as  the  motion 
of  the  wave. 

414.  Kinds  of  Wave  Motion.  There  are  two  kinds  of  wave 
motion:  (a)  transverse  and  (b)  longitudinal. 

A  transverse  wave  is  one  in  which  the  vibrating  particles  move 
at  right  angles  to  the  direction  of  the  motion  of  the  wave.  A 
good  illustration  of  transverse  waves  are  those  seen  on  the 
surface  of  the  water;  also  a  series  of  waves  traveling  along  a 
rope  or  string. 

A  longitudinal  wave  is  one  in  which  the  vibrating  particle 
moves  back  and  forth  in  the  same  direction  as  the  motion  of 

A  B  a 


o  o     o    o   o  oooo  o 

RAREFACTION  CONDENSATION 

FIG.  386 

the  wave.  Longitudinal  waves  may  also  be  illustrated  by  a 
row  of  balls  suspended  as  shown  in  Fig.  386.  If  a  disturbance 
be  set  up  by  striking  ball  A,  it  will  be  passed  along  from  ball 
to  ball  until  the  disturbance  has  run  the  length  of  the  line. 
This  illustrates  a  longitudinal  wave,  which  consists  of  a  con- 
densation and  rarefaction.  As  the  wave  runs  forward  from  A 
to  C  there  is  a  point  where  the  particles  are  crowded  together. 
This  is  called  a  condensation.  At  the  point  B  the  particles 
have  begun  to  swing  back  toward  A]  this  portion  of  the 
wave  is  called  a  rarefaction.  A  condensation  and  a  rarefaction 
together  constitute  the  entire  wave. 

415.  Relation  of  the  Medium  to  the  Kind  of  Wave  Trans- 
mitted. Substances  like  solids,  which  possess  rigidity,  are  cap- 
able of  transmitting  both  transverse  and  longitudinal  waves.  For 
example,  if  a  steel  rod  clamped  in  the  middle,  as  shown  in  Fig. 
387,  be  plucked  at  one  end  it  will  vibrate  transversely;  that  is, 


SOUND 


277 


FIG.  388 


the  motion  of  the  rod  is  at  right  angles  to  its  length.  The 
same  rod  may  also  be  made  to  transmit  longitudinal  waves. 
If  it  be  stroked  lightly  about  one-fourth  the  distance  from  the 
end  with  a  soft  piece  of 
leather  upon  which  there 
has  been  dusted  some  pow- 
dered resin,  the  rod  will 
give  forth  a  distinct  note  FIG.  337 

of  high  pitch,  and  a  light 

ivory  ball  suspended  at  one  end  will  be  thrown  out  vigorously, 
as  shown  in  Fig.  388.  Longitudinal  waves  consisting  of  con- 
densations and  rarefac- 
tions run  the  length  of 
the  rod  from  one  end 
to  the  other  and  back 
again,  as  shown  by  the 
motion  of  the  ball. 

Substances  which  do 
not  possess  rigidity,  such  as  fluids  (air  and  water,  for  example), 
are  capable  of  transmitting  only  longitudinal  waves;  that  is, 
waves  consisting  of  condensations  and  rarefactions.  Sound 
waves  in  air  or  in  water,  then,  are  transmitted  by  longitudi- 
nal waves.  It  must  be  noted  here  that  while  a  wave  in 
water  is  an  example  of  a  longitudinal  wave,  a  wave  on  the 
surface  of  the  water  is  an  example  of  a  transverse  wave. 

416.  Wave  Length  and  Amplitude.  A  wave  length  is  the 
distance  measured  in  a 
straight  line  from  any  point 
in  a  given  wave  to  the  cor- 
responding  point  in  the  next 
wave.  In  transverse  waves 
we  usually  measure  the 

wave  length  from  crest  to  crest  or  from  trough  to  trough,  as 
from  a  to  b,  Fig.  389.  In  longitudinal  waves  we  measure  the 
wave  length  from  condensation  to  condensation  or  from  rare- 


FIG.  389 


278 


HIGH   SCHOOL   PHYSICS 


faction  to  rarefaction.  A  wave  length,  however,  is  not  neces- 
sarily measured  from  crest  to  crest  or  from  condensation  to 
condensation;  it  may  be  measured  from  any  point  in  a  wave 
to  the  corresponding  point  in  the  next  wave. 

The  amplitude  of  vibration  is  one-half  the  distance  through 
which  a  particle  swings  as  the  wave  runs  under  it.  In  transverse 
waves  the  amplitude  is  measured  at  right  angles  to  the  direc- 
tion of  propagation  of  the  wave,  ac  and  de,  Fig.  389.  In  longi- 
tudinal waves  amplitude  is  measured  in  the  same  line  as  the 
direction  of  propagation  of  the  wave.  In  the  case  of  the  swing- 
ing balls  the  amplitude  of  vibration  is  one-half  of  the  space 
swept  by  the  swing  (vibration)  of  any  individual  ball. 

J  TRANSMISSION  OF  SOUND 

417.  Sound  Waves  Transmitted  in  all  Directions.  Just  as 
the  transverse  surface  water  waves  travel  out  in  concentric 
circles  in  all  directions  over  the  surface  from  the  point  of  dis- 
turbance, so  in  a  somewhat  similar  manner  sound  waves  in 
air  travel  outward  in  the  form  of  condensations  and  rarefac- 
tions from  the  point  of  disturbance  in  a  series  of  concentric 
spherical  shells.  Suppose,  for  example,  a  bell  be  struck.  As 
it  vibrates  it  sets  up  a  series  of  condensations  and  rarefactions 
which  travel  outward,  as  shown  in  Fig.  390.  These  waves 


FIG.  390 


FIG.  391 


SOUND  279 

striking  upon  the  ear  produce,  due  to  the  change  of  pressure 
caused  by  the  condensations  and  rarefactions,  a  disturbance 
in  the  organs  of  hearing  which  give  rise  to  the  sensation  of 
hearing. 

418.  Sound   Waves   not   Transmitted    through   a   Vacuum. 
The  characteristics  of  a  medium  suitable  for  the  transmission  of 
sound  waves  are  as  follows:    (a)  The  medium  must  be  elastic, 
(b)   continuous,  and    (c)   ponderable,  that  is,  it  must   have 
weight. 

Experiment.  If  an  electric  bell  be  placed  within  a  bell  jar, 
Fig.  391,  and  the  circuit  be  closed,  the  ringing  of  the  bell  can 
be  distinctly  heard.  If  now  the  air  be  exhausted  from  the 
bell  jar,  the  sound  of  the  bell  becomes  fainter  and  fainter,  and 
finally  dies  away  altogether.  Sound  waves  will  not  travel 
through  a  vacuum,  for  the  reason  that  it  has  no  medium  fulfill- 
ing the  characteristics  named  above. 

419.  Velocity  of  Sound.      The  velocity  of   sound    in   any 
medium  depends  upon  two  factors:   (a)  the  elasticity  of  the 
medium  and  (b)  its  density.      The  greater  the  coefficient  of 
elasticity  e  of  the  medium,  the  greater  the  velocity;   also,  the 
greater  the  density  of  the  medium  d,  the  less  the  velocity.     The 
relation  of  the  velocity  of  sound  to  these  two  factors  is  ex- 
pressed definitely  by  the  equation 


velocity  =  \/ coefficient  of  elasticity / density 
v  =  Ve/d 

Example.  If  the  velocity  of  sound  in  a  given  medium  under 
given  conditions  of  elasticity  and  density  be  1000  feet  per 
second,  how  will  the  velocity  be  affected  if  the  coefficient  of 
elasticity  be  increased  fourfold  and  the  density  be  increased 
from  1  to  16?  Solution:  1000:  v  =  VlA  :  V4/16;  hence  v  = 
500  feet  per  second. 

420.  Velocity  of  Sound  in  Different  Media.  The  velocity  of 
sound  in  air  was  first  determined  by  two  observers  stationing 
themselves  several  miles  apart.  A  cannon  was  fired  by  one, 


280  HIGH   SCHOOL  PHYSICS 

and  the  other  observed  the  flash  and  counted  the  number  of 
seconds  required  for  the  sound  to  reach  him,  it  being  assumed 
that  the  time  required  for  the  light  to  travel  from  the  cannon 
to  the  observer  was  so  small  as  to  be  negligible.  In  this  way  a 
calculation  of  the  velocity  of  sound  in  air  was  made.  Many 
later  experiments  have  been  devised  and  carried  out  to  deter- 
mine accurately  the  velocity  of  sound  in  different  media. 

The  velocity  of  sound  in  air  at  0°  C.  is  1090  feet,  or  ^332jneters_ 
per  second. 

The  velocity  of  sound  in  water  at  4°  C.  is  4674  feet  per  sec- 
ond. That  is,  the  velocity  of  sound  in  water  is  about  four  times 
the  velocity  of  sound  in  air. 

The  velocity  of  sound  in  steel  is  16,500  feet  per  second,  about 
fourteen  times  the  velocity  of  sound  in  air. 

The  reason  the  velocity  of  sound  in  liquids  and  solids  is 
greater  than  that  in  air  is  due  to  the  fact  that  the  coefficient  of 
elasticity  of  liquids  and  of  solids  is  very  many  times  greater 
than  that  of  air, 

421.  Relation  of  Temperature  to  Velocity.     An  increase  in 
temperature  causes  an  increase  in  the  velocity  of  sound.     The 
reason  for  this  will  be  made  clear  when  we  consider  the  equa- 
tion v  =  \/e/d.     When  air,  which  is  free  to  expand,  is  heated, 
its  elastic  properties  remain  unchanged  while  its  density  is 
diminished,  and  thereby  the  value  of  v  is  increased.     On  the 
other  hand,  if  the  air  be  confined  in  a  vessel  of  constant  vol- 
ume and  heated,  it  could  not  expand,  hence  there  would  be  no 
change  in  the  density,  but  the  coefficient  of  elasticity  would 
be  increased,  and  as  a  result  the  value  of  v  would  again  be  in- 
creased.    Thus  we  see  that  a  change  in  temperature  causes  an 
increase  in  the  velocity  of  sound. 

An  increase  in  temperature  of  1°  C.  causes  an  increase  in 
velocity  of  sound  in  air  of  (a)  2  feet,  or  (6)  0.6  meter  per  second. 

422.  Reflection  of  Sound.     When  sound  waves  strike  against 
an  obstructing  medium,  such  as  the  face  of  a  cliff,  the  wall  of  a 
building,  the  trees  of  a  forest,  or  even  against  the  vapors  of  a 


SOUND  281 

cloud,  they  are  reflected  ;  that  is,  they  bound  off,  as  does  a  ball 
when  thrown  against  a  wall.  Sound  waves  reflected  from  a 
smooth  concave  surface  may  be  brought  to  a  focus  by  a 
similar  concave  surface  as  _ 

shown    in    Fig.    392.     The      \ 
ticking  of  a  watch  placed 


at    a    may    be    distinctly    \  y 

heard     at     6,    although    it      ^  FIQ  3Q2 

may   be   entirely  inaudible 

at  c,  midway  between  the  two.     The  reflection  of  the  sound  is 

illustrated  in  the  use  of  the  speaking  tube  and  in  the  case  of 

the  echo. 

423.  The  Echo.     If  a  person  call  at  a  distance  from  a  reflect- 
ing medium,  in  a  very  short  time  his  voice  will  be  returned  to 
him  in  an  echo.     The  echo  is  due  to  the  fact  that  the  sound 
waves  traveling  outward  strike  against  the  medium  and  are 
reflected  back  to  the  source.     The  echo  is  never  as  loud  as  the 
original  sound  because  a  portion  of  the  energy  of  the  wave  is 
always  lost  by  absorption  at  the  reflecting  surface  and  a  small 
portion  is  also  lost  in  traveling  from  the  person  to  the  reflect- 
ing medium  and  back  again.     Since  the  sensation  of  sound 
lasts  for  one-tenth  of  a  second,  it  follows  that  in  order  to 
hear  an  echo  of  one's  voice  it  is  necessary  to  stand  far  enough 
away  from  the  reflected  surface  so  that  more  than  one-tenth  of 
a  second  will  elapse  between  the  origin  of  the  sound  and  its 
return.     Since  sound  travels  at  the  rate  of  about  1100  feet  per 
second,  it  would  therefore  be  necessary  to  stand  at  a  distance 
greater  than  55  feet  from  the  reflecting  surface  in  order  to  hear 
the  echo. 

424.  Refraction  of  Sound.     Sound  waves  may  be  refracted. 
Refraction  is  the  change  of  direction  of  the  motion  of  a  wavcp 

due  to  its  passage  from  a  medium  of  one  density  to  a  medium 
of  different  density^  For  example,  if  a  series  of  sound  waves 
originating  at  the  point  A,  Fig.  393,  strike  against  the  balloon 
shaped  body  B,  containing  carbon  dioxide,  which  is  more 


282 


HIGH  SCHOOL  PHYSICS 


dense  than  air,  the  waves  will  be  bent  in  such  a  way  that  the 
sound  will  come  to  a  fo'cus  at  C.  This  may  be  readily  under- 
stood when  we  consider  what  will  happen  to  the  portion  of  the 

wave  marked  ab.  Since 
b  gets  into  the  dense  me- 
dium first,  its  speed  is  re- 
tarded, hence  the 'line  of 
direction  is  bent  down- 
ward, as  shown;  a  gets 
out  of  the  medium  first, 
FIG.  393  and  hence  travels  with  a 

greater  speed  than  6,  thus 

bending  the  wave  further  towards  C.  Of  course  when  both 
portions  of  the  wave  get  into .  the  air  they  travel  with  the 
same  velocity.  If  the  balloon  shaped  vessel  were  filled  with 
a  gas  lighter  than  air,  such  as  hydrogen,  the  waves,  instead  of 
converging  and  coming  to  a  focus  as  shown,  would  diverge. 


LOUDNESS   AND    INTENSITY   OF   SOUND 

425.  Loudness  of  Sound.  The  loudness,  or  intensity  ofx 
sound,  depends  upon  four  factors:  (a)  the  amplitude  of  vibra- 
tion, (b)  the  distance  of  the  sounding  body  from  the  ear,  (c) 
the  density  of  the  medium,  and  (d)  the  area  of  the  sounding 
body.  The  distinction  between  intensity  and  loudness  lies  in 
this:  Intensity  depends  upon  the  energy  of  the  vibrating  par- 
ticle; loudness  depends  not  only^  upon  the  energy  of  the  vibra- 
tion, but  also  upon  the  nature  of  the  hearing  apparatus,  the 
ear.  Thus  two  persons  may  hear  a  sound  of  given  intensity 
with  a  different  degree  of  loudness.  For  a  given  ear  a  change 
in  intensity  produces  a  change  in  the  loudness  with  which  the 
sound  is  heard;  a  change  in  loudness,  on  the  other  hand,  does 
not  necessarily  imply  a  change  in  intensity,  since  loudness 
depends  both  upon  the  intensity  and  upon  the  /nature  and 
condition  of  the  hearing  apparatus. 


SOUND  283 

426.  Relation  of  Intensity  to  Amplitude  of  Vibration.     Ex- 
periment.    If,  for  example,  the  prongs  *of  a  tuning  fork  be 
tapped  lightly  so  that  they  vibrate  through  a  very  small  arc, 
a  faint  sound  is  heard ;  ^if  now  they  be  struck  sharply,  so  that  the 

.prongs  vibrate  through  a  very  much  larger  arc,  they  give  off 
a  sound  much  louder  than  the  first.  It  can  thus  be  shown 
that  the  intensity  of  sound  varies  directly  as  the  square  of  the 
amplitude  of  the  vibrating  body.  If  a  vibrating)  body  having 
an  amplitude  of  one  .unit  produce  a  sound  of  given  intensity, 
then  if  the  body  be  made  to  vibrate  through  an  amplitude 
of  two  units,  the  intensity  will  be  four  times  as  great. 

427.  Relation  of  Intensity  to  Distance.     Intensity  varies  in- 
versely as  the  square  of  the  distance.     It  is  a  common  experience 
that  if  we  walk  away  frpm  a  sounding  body  the  loudness 
decreases  as  the  distance  increases.     It  can  be  demonstrated 
both    experimentally    and    mathematically  that  the  intensity 
varies    inversely,  as   the   square   of   the   distance    from   the 
source.     Consider  that  a'  cannon  be  fired  at  C,  Fig.  394.    We 


CANNON  1  MILE  SMILES 

FIG.  394 

wish  to  compare  the  intensity  of  the  sound  at  A,  distant  one 
mile  from  C,  with  the  intensity  of  the  sound  at  B,  distant 
three  miles.  '  Since  intensity  varies  inversely  as  the  square  of 
the  distance,  the  intensity  at  A  will  be  nine  times  as  great  as 
at  B;  that  is,  /:  /'  =  32:  I2. 

428.  Intensity  Depends  upon  the  Density  of  the  Medium. 
The  denser  the  medium  the  louder  the  sound;  the  rarer  the 
medium,  the  less  loud  the  sound.  As  one  ascends  in  a  balloon, 
the  air  becomes  rarer  and  rarer  as  the  distance  from  the  earth 
increases  and  the  loudness  of  the  sound,  therefore,  diminishes. 
If,  on  the  other  hand,  a  person  were  to  go  into  a  deep  mine 
or  down  in  a  diving  bell,  the  sound  of  the  human  voice  would 


284  HIGH   SCHOOL   PHYSICS 

be  much  louder  than  at  the  surface  of  the  earth,  due  to  the 
increase  in  density. 

429.  Relation  of  Intensity  to  Area.     Intensity  depends  upon 
the  area  of  the  vibrating  body.     Experiment.     If  a  tuning  fork 
be  set  in  vibration  and  held  in  one  hand,  a  sound  of  a  given 
loudness  will  be  heard.     Now  if  the  tuning  fork,  while  still  in 
vibration,  be  placed  in  contact  with  the  top  of  the  desk  or 
upon  a  resonance  box,  the  sound  will  at  once  become  very 
much  louder,  due  to  the  fact  that  a  body  of  increased  area  is 
set  in  vibration. 

RESONANCE  AND  INTERFERENCE 

430.  Free  Vibrations.     The  vibration  of  a  pendulum  free 
from  all  influences,  except  that  due  to  the  attraction  of  grav- 
ity, is  an  example  of  a  free  vibration.     If  there  were  no  fric- 
tion, the  pendulum  would  continue  to  vibrate  forever.     As  it 
is,  however,  all  freely  vibrating  bodies   sooner  or  later  come 
to  rest,  due  to  the  damping  effect  of  the  friction  of  the  medium 
in  which  they  swing.     Examples  of  free  vibrations  are  seen 
in  the  motion  of  the  pendulum,  as  described  above,  also  in  the 
motion  of  a  guitar  string,  or  in  that  of  a  tuning  fork. 

431.  Force    Vibrations.     When    a    body    vibrates    not    in 
response  to  its  own  nature  but  in  response  to  some  periodic 
force  applied  to  it,  we  have  what  is  called  a  forced  vibration.     A 
good  illustration  of  a  forced  vibration  is  that  of  the  motion  of 
the  pendulum  of  a  clock  or  the  balance  wheel  of  a  watch,  in 
which  case  the  vibrating  bodies  move  in  response  to  a  periodic 
force  applied  to  the  weights  or  spring.     Other  examples  of 
forced  vibrations  are  those  of  the  sounding  board  of  a  piano, 
or  the  body  of  a  violin,  or  the  case  of  the  desk  when  the  stem 
of  the  tuning  fork  is  pressed  upon  it. 

432.  Resonance.     When  the  period  of  the  vibrating  body 
is  the  same  as  that  of  the  impressed  force  we  have  a  special 
case  of  forced  vibration  known  as  resonance.     If,  for  example, 
two  tuning  forks  of  the  same  period  be  mounted  near  to  each 


SOUND  285 

other,  Fig.  395,  and  one  set  in  vibration  and  after  a  few  moments 
stopped,  it  may  be  observed  that  the  other  fork  is  vibrating, 
as  may  be  demonstrated  by  a  light  ivory  ball  suspended  so 
as  just  to  touch  the  fork.  This  is  due  to  the  fact  that  the 
impulses  of  the  air  from  the  first  fork  act  upon  the  second,  and 
since  its  period  of  vibration  j 

is  the  same  as  that  of  the 
impulses  impressed  upon  it, 
it  responds.  A  further  illus- 
tration of  the  relation  of  the 
impressed  force  to  the  period 
of  the  vibrating  system  is 

seen  in  the  case  of  the  swing.  ^ 

-T  iG..oyo 
A    little    child    may    set    a 

heavy  swing  in  vibration,  provided  the  impulses  (pushes)  be 
so  timed  as  to  coincide  with  the  period  of  vibration  of  the 
swing.  First  the  swing  moves  through  a  very  small  arc,  but 
soon  it  responds  to  the  periodic  impulses,  and  may  after  a 
time  swing  through  a  large  arc.  The  motion  of  the  swing  is  an 
example  of  a  forced  vibration,  and  since  its  period  of  vibration 
coincides  with  the  impulses  imparted  by  the  child,  we  have  a 
case  of  resonance. 

A  striking  illustration  of  resonance  is  that  of  the  vibration 
of  a  bridge,  due  to  the  footfalls  of  a  small  dog  running  across 
it.  If  the  period  of  the  impulses  imparted  by  the  dog  agree 
with  the  period  of  the  bridge,  the  latter  will  be  set  in  vibration. 
Soldiers  when  crossing  a  bridge  are  commanded  to  break  step, 
to  avoid  the  possibility  of  doing  damage  to  the  structure,  due 
to  the  resonance  in  response  to  the  regular  steps. 

433.  Resonators.  Experiment.  A  tube  so  adjusted  that  the 
air  within  it  vibrates  in  unison  with  some  outside  vibrating 
body,  such  as  a  tuning  fork,  is  called  a  resonator.  If  a  glass 
tube,  Fig.  396,  be  partly  immersed  in  water  and  moved  up 
and  down  while  a  fork  vibrates  about  it,  there  will  be  found  a 
certain  point  at  which  the  tube  will  respond  to  the  fork;  that 


286 


HIGH  SCHOOL  PHYSICS 


FIG.  396 


is,  the  resonance  tube  will  give  out  a  relatively  loud  sound. 
Now  if  a  fork  having  a  different  vibration  rate  be  held  above 
the  tube,  no  response  is  heard.  If,  however,  the  tube  be  moved 

up  or  down,  there  will  be  found 
another  point  at  which  it  will 
respond  to  the  second  fork. 
Thus  each  fork  requires  a  tube 
of  a  certain  length  to  be  in  reso- 
nance with  it.  This  illustrates 
resonance  in  the  case  of  a  tube 
closed  at  one  end,  as  by  the 
water.  Resonance  for  a  given 
fork  may  also  be  obtained  from 
a  tube  open  at  both  ends,  pro- 
vided the  tube  be  twice  the 
length  of  the  closed  tube,  Fig. 
397. 

434.  Explanation  of  Reso- 
nance in  a  Tube.  Let  a,  6,  c 
represent  the  motion  of  one 
prong  of  a  tuning  fork  which  is 
vibrating  at  the  mouth  of  a  closed  resonance  tube,  so  adjusted 
as  to  respond  to  the  fork.  As  the  prong  of  the  fork  moves 
from  a  to  b  a  condensation  is  sent  down  into  the  tube.  While 
the  fork  moves  from  b  to  c  and  comes  to  rest  for  a  moment  in 
changing  its  direction  of  motion,  the  condensation  has  time  to 
run  down  the  tube,  strike  the  water,  be  reflected,  and  get  back 
to  c  in  time  to  join  the  new  condensation  which  is  formed  as 
the  fork  moves  from  c  toward  b.  The  condensations  and 
rarefactions  which  are  reflected  from  the  bottom  of  the  tube 
coincide  with  the  condensations  and  rarefactions  of  the  sound 
waves  given  off  by  the  fork,  thus  producing  a  reinforcement  of 
the  sound,  and  hence  giving  rise  to  an  increase  in  loudness. 

435.    Relation  of  the  Length  of  a  Wave  to  Length  of  Reso- 
nance Tube.     Let  us  consider  again  the  case  of  a  resonance 


FIG.  397 


SOUND  287 

tube  which  is  closed  at  one  end  and  which  is  responding  to  a 
given  fork.  A  sound  wave  travels  one  wave  length  while  the 
fork  makes  one  complete  vibration.  Now  we  have  learned  that 
during  one  complete  vibration  of  the  fork  a  condensation  travels 
twice  the  length  of  the  tube  (down  and  back),  and  a  rarefac- 
tion likewise  travels  twice  the  length  of  the  tube.  A  sound 
wave  consists  of  a  condensation  and  rarefaction  each  of  which, 
during  one  complete  vibration  of  the  fork,  travels  twice  the 
length  of  the  resonance  tube.  It  follows,  therefore,  that  a 
closed  resonance  tube  sounding  its  lowest  note  is  one-fourth 
the  wave  length  of  the  corresponding  sound  wave  in  air. 

It  may  be  shown  in  a  somewhat  similar  manner  that  an  open 
resonance  tube  sounding  its  lowest  note  is  one-half  the  wave 
length  of  the  corresponding  wave  length  in  air. 

436.  Relation  of  Wave  Length  to  Velocity  and  Number  of 
Vibrations.     Suppose  that  the  fork  is  making  256  vibrations 
per  second  and  we  desire  to  find  the  wave  length  of  the  corre- 
sponding sound  waves  in  air  when  the  temperature  is  20°  C. 
Now  the  velocity  of  sound  at  20°  C.  is  1130  feet  per  second. 
While  the  fork  is  making  256  vibrations  sound  travels  a  dis- 
tance of  1130  feet.     This  means  that  in  a  space  of  1130  feet 
there  are  256  waves.      Therefore,  the  length  of  one  wave  = 
~f~  =  4.4  feet.     It  follows  then  that  the  length  of  a  wave  in 
an  elastic  medium  is  represented  by  the  equation 

velocity 

wave  length  = =- -r-~ — —. — 

number  of  vibrations 

I  =  v/n 

in  which  I  is  the  wave  length,  v  the  velocity  of  the  sound  in  air, 
and  n  the  frequency,  that  is,  the  number  of  vibrations  per 
second. 

437.  How  to  Measure  Wave  Length  and  Number  of  Vibra- 
tions  by  Means    of   a  Resonance  Tube.       It  is  possible  by 
means  of  a  resonance  tube  to  measure  with  a  reasonable  degree 
of  accuracy  the  wave  length  of  the  sound  given  off  by  a  tuning 


288  HIGH  SCHOOL  PHYSICS 

fork,  and  also  to  determine  the  number  of  vibrations  of  the 
fork,  that  is,  its  frequency.  Suppose  that  we  wish  to  deter- 
•  mine  the  wave  length  and  the  number  of  vibrations  per  second 
of  a  given  tuning  fork.  A  glass  tube  one  end  of  which  is 
thrust  into  water,  as  already  explained,  serves  as  a  resonance 
tube.  The  given  fork  is  set  in  vibration  and  held  above  the 
tube,  which  is  moved  up  and  down  until  the  point  of  resonance 
is  reached.  We  now  measure  the  distance  from  the  fork  to 
the  water,  which  represents  the  length  of  the  closed  resonance 
tube.  Four  times  this  length  equals  the  wave  length  of  the 
corresponding  sound  in  air. 

Now  by  means  of  the  relation,  I  =  v/n,  we  may  at  once  deter- 
mine n,  the  number  of  vibrations  per  second.  Suppose  the 
temperature  at  which  the  experiment  is  carried  out  is  26°  C. 
and  that  the  length  of  the  resonance  tube  is  10.5  inches.  At  a 
temperature  of  26°  C.  the  velocity  of  sound,  v,  in  air  =  1090  + 
(2  X  26)  =  1142  feet  per  second;  and  wave  length  I  =  4  X 
10.5  inches  =  42  inches  =  3.5  feet.  Now  using  the  equation 
above,  we  may  write 

n  =  -5-^-  =  326  vibrations  per  second 
o.o  , 

Example.  A  closed  resonance  tube  18  inches  in  length 
responds  to  a  given  fork,  the  temperature  of  the  air  being  20° 
C.  Find  the  vibration  rate  of  the  fork.  Solution:  Wave 
length,  I  =  4  X  1.5  =  6  feet;  velocity  of  sound,  v}  at  20°  C.  = 
1090  +  40  =  1130  feet  per  second.  Then  from  the  equation 
I  =  v/n  we  may  write  n  =  1130/6  =  188.3  feet  per  second. 

EXERCISES.  1.  A  resonance  tube  1  ft.  in  length  responds  to  a  fork 
making  288  vibrations  per  second.  Find  (a)  the  velocity  of  sound  corre- 
sponding to  the  conditions  of  the  experiment;  (b)  the  temperature. 

2.  Find  the  length  of  a  closed  pipe  that  will  respond  to  a  fork  making 
256  vibrations  when  the  temperature  is  10°  C. 

3.  Determine  the  pitch  of  a  fork  that  is  in  resonance  with  a  closed  tube 
15  in.  in  length  at  0°  C. 


SOUND  289 

438.    Reinforcement    and    Interference    of    Sound.     If   two 

sound  waves  occur  together  so  that  the  condensations  and 
rarefactions  of  one  coincide  with  the  condensations  and  rare- 
factions of  the  other,  the  resulting  sound  will  be  louder  than 
either  of  the  sounds  producing  it.  In  Fig.  398  is  shown  in  a 


FIG.  398 

graphic  way  the  result  of  adding  two  sound  waves,  as  has  just 
been  described.  The  resultant  sound  wave  is  represented  by 
the  line  having  an  amplitude  greater  than  either  of  the  other 
waves. 

On  the  other  hand,  if  two  sound  waves  be  superimposed  one 
upon  the  other,  so  that  the  condensation  of  one  coincides  with 
the  rarefaction  of  the  other,  the  result  will  be  a  diminution  in 
loudness.  Indeed  it  is  possible  for  two  sound  waves  to  be  so 
impressed  one  upon  the  other  that  silence  will  result.  This  con- 
dition is  shown  in  Fig.  399,  in  which  is  represented  graphically 


FIG.  399 

two  sound  waves  of  the  same  wave  length  and  amplitude, 
the  condensations  of  one  coinciding  exactly  with  the  rarefac- 
tions of  the  other.  The  resultant  is  represented  by  the 
straight  line,  which  indicates  silence. 

Tine  amplitude  of  the  resultant  sound  wave  is  at  every  point 
equal  to  the  algebraic  sum  of  the  amplitudes  of  the  original  sound 
waves  producing  it. 


290 


HIGH   SCHOOL   PHYSICS 


439.  Beats.  Suppose  that  we  have  two  sound  waves  of 
different  lengths  traveling  in  the  same  direction,  as  shown  in 
Fig.  400.  At  the  points  A  and  C  the  waves  coincide  in  such 


A 


FIG.  400 

a  way  that  they  reinforce  each  other.     At  B  they  interfere  in 
such  a  way  as  partially  to  annul  each  other.     The  resultant 

wave  is  represented  by  the 
line  A'B'C'.  At  the  points 
A'  and  C'  the  sound  will  be 
loud;  at  the  point  Bf  it  will 
be  faint,  thus  producing  a 
rise  and  fall  in  loudness. 
This  periodic  increase  and 
decrease  in  loudness  due  to 
the  interference  of  two 
sound  waves  is  called  beats. 
440.  Illustration  of  Beats. 
Experiment.  A  striking  il- 
lustration of  beats  occurs  in 
connection  with  the  singing 
flame.  Let  two  jets  of  flame 
be  prepared  as  shown  in  Fig. 
401.  First,  over  one  of  the  flames  place  a  glass  tube  about  2 
feet  in  length  and  from  three-quarters  to  an  inch  in  diameter. 
Move  the  tube  up  and  down  until  a  certain  position  is  found 


FIG.  401 


SOUND  291 

in  which  the  flame  will  sing,  due  to  the  ^sympathetic  vibrations 
set  up  in  the  tube  by  the  fluttering  of  the  flame.  Now  over 
the  second  flame  place  a  second  tube  B,  having  around  one  end 
a  cylinder  of  paper  which  may  be  moved  up  or  down  as  the 
case  may  require.  The  paper  slider  may  be  adjusted  until  the 
point  is  reached  at  which  the  second  tube  produces  a  singing 
noise.  Now  if  the  wave  length  given  out  by  the  two  tubes 
be  somewhat  different,  a  very  beautiful  illustration  of  inter- 
ference (beats)  occurs.  A  distinct  throbbing  sound  will  be 
heard  due  to  the  interference  of  the  two  wave  trains. 

The  number  of  beats  which  occur  per  second  is  equal  to  the 
difference  in  frequency  of  the  two  sounding  bodies. 

PITCH  AND  Music 

441.  Pitch.  The  pitch  of  a  sound  depends  upon  the  num- 
ber of  vibrations  of  the  sounding  body.  When  the  number 
of  vibrations  per  second  is  great,  the  pitch  is 
high;  when  small,  the  pitch  is  low.  If  two 
sounds  are  produced  by  the  same  number  of 
vibrations  per  second,  they  are  said  to  have 
the  same  pitch,  and  if  sounded  together  they 
are  said  to  be  in  unison. 

442  The  Siren.  Experiment.  The  siren  is 
an  instrument  for  illustrating  and  determining 
pitch.  It  consists  of  a  circular  disc  having 
several  rows  of  holes,  as  shown  in  Fig.  402, 
mounted  so  as  to  be  rotated  at  some  given 
speed.  Now  let  air  be  blown  against  the  disc 
through  a  tube.  When  one  of  the  holes  of  the 
rotating  disc  comes  in  front  of  the  tube,  a  puff 
of  air  goes  through,  thus  producing  a  con- 
densation; at  the  next  instant  the  stream  of  FIG.  402. —  Siren 
air  is  shut  off  by  the  disc,  which  produces 
something  corresponding  to  a  rarefaction.  Now  if  the  disc 
be  rotated  at  a  given  speed,  and  the  tube  through  which  the 


292  HIGH  SCHOOL   PHYSICS 

air  is  blown  be  slowly  moved  from  the  center  of  the  disc  out- 
ward, a  series  of  sounds  will  be  produced  which  increase  in 
pitch,  due  to  the  fact  that  the  number  of  holes  increase  from 
center  to  circumference.  To  determine  the  pitch  of  any  sound, 
as  given  by  the  siren,  we  would  have  to  know  the  number  of 
holes  in  the  particular  series  in  front  of  the  tube,  and  also  the 
number  of  revolutions  of  the  disc  per  second.  For  example, 
suppose  that  in  the  outside  row  there  are  48  holes  and  the  disc 
is  making  10  revolutions  per  second.  This  will  give  10  X  48 
=  480  condensations  and  rarefactions;  that  is,  480  vibrations 
per  second. 

443.  The  Use  of  the  Siren.     If  a  siren  be  provided  with  an 
apparatus  that  will  count  automatically  the  number  of  revolu- 
tions per  second,  it  is  possible  by  means  of  this  instrument  to 
determine  the  number  of  vibrations  of  a  given  sound,  provided 
the  operator  is  able  to  tell  by  ear  when  the  two  sounds,  that  of 
the  siren  and  that  of  the  given  body,  are  in  unison.     Suppose 
for  illustration  we  wish  to  determine  the  number  of  vibrations 
made  by  the  wings  of  a  bee  buzzing  on  the  window  pane.     The 
siren  is  rotated  until  the  pitch  of  the  instrument  coincides  with 
that  of  the  wings  of  the  insect.     At  this  -instant  the  number 
of  revolutions  per  second  is  noted,  which  multiplied  into  the 
number  of   holes   passing  before  the  tube  gives  the  number 
of  vibrations  per  second  required.     In  a  similar  manner  the 
number  of  vibrations  of  any  instrument,  such  as  a  tuning  fork, 
may  be  determined. 

444.  Musical    Sounds.     Musical    sounds    are    those    which 
have  a  definite  pitch  and  which  produce  a  pleasing  effect  upon 
the  ear.     A  noise  is  a  combination  of  sounds  in  which  the  ear 
is  unable  to  detect  a  definite  pitch,  as  in  the  confusion  of  sounds 
arising  from  street   traffic  or  in  the  clatter  of  machinery  in  a 
factory. 

The  essential  features  of  music  lie  in  the  elements  (a)  definite- 
ness  of  pitch,  (b)  periodicity,  (c)  agreeableness  to  the  ear.  A 
series  of  sounds  may  be  periodic  and  have  a  definite  pitch 


SOUND 


293 


and  yet  not  be  pleasing  to  the  ear,  as  in  the  case  of  the  beat- 
ing of  the  tom-tom  in  an  oriental  temple,  or  in  the  monoto- 
nous cries  which  accompany  an  Indian  war  dance.  Occidental 
or  western  music  differs  from  oriental  music  mainly  in  the 
character  of  the  sounds  which  are  selected  as  being  pleasing  to 
the  ear. 

445.  Some  Musical  Terms,  (a)  A  note,  as  used  in  a  musical 
sense,  may  refer  to  a  sound  having  a  definite  pitch  or  to  a  sym- 
bol in  an  arbitrary  scale.  The  word  tone  is  often  used  in  the 
same  sense  as  the  word  note,  referring  to  a  sound  of  a  definite 
pitch;  or,  on  the  other  hand,  it  may  refer  to  the  sound  result- 
ing from  a  number  of  notes. 

(6)  A  musical  interval  is  the  ratio  of  the  pitch  (vibration 
number)  of  a  given  note  to  the  pitch  of  another  note.  For 
example,  the  interval  expressed  by  the  ratio  1 :  1  is  called  uni- 
son; that  expressed  by  the  ratio  2:1,  an  octave.  Thus  if  one 
note  have  a  pitch  due  to  256  vibrations  per  second,  and 
another  512  vibrations  per  second,  we  say  that  the  pitch 
of  the  second  is  an  octave  higher  than  the  first. 

(c)  When  any  three  notes  having  a  ratio  4:5:6  are  sounded 
together  they  produce  a 
tone  which  is  pleasing  to 
the  ear;  the  same  is  true 
also  of  the  ratios  10:12: 15. 
A  major  chord  consists  of 
four  notes  having  a  ratio 
4:5:6:8,  represented  in 
music  as  do,  mi,  sol,  do'. 
In  Fig.  403  there  is  shown 
a  set  of  four  forks  which 
sounding  together  give  a 
major  chord.  A  minor  FlG  4Q3 

chord  consists  of  four  notes 

having  the  ratios  10  :  12  :  15  :  20.  From  the  major  and  minor 
chords  we  derive  our  musical  scales. 


294 


HIGH   SCHOOL  PHYSICS 


446.  The  Diatonic  Scale.  The  diatonic  scale,  or  gamut,  as 
it  is  sometimes  called,  consists  of  a  series  of  eight  notes  having 
definite  ratios.  The  gamut  derived  from  the  major  chord, 
based  upon  the  ratios  4:5:6,  is  called  the  major  diatonic  scale; 
that  based  on  the  minor  chord  is  called  the  minor  diatonic 
scale.  Below  is  given  the  major  diatonic  scale  in  the  key  of 
C,  Fig.  404. 


1 

I 

y 

/\\ 

| 

_J 

a 

(  \) 

1 

-. 

2 

I 

^ 

^ 

Cx 

Name 

-0- 
DO 

o 

RE 

Ml 

FA 

SOL 

LA 

Tl 

DO 

Letter 

C 

D 

E 

F 

G 

A 

B 

c' 

Ratio 

1 

0 

5/4 

4/3 

3/2 

5/3 

15/8 

2 

Interval 

9/ 

^8         1(X 

'9         18/ 

'15        ^ 

*          1? 

/9         9/ 

8           16X 

<5 

FIG.  404.  —  Diatonic  Scale 

Intervals  between  two  consecutive  notes  having  the  ratios  of 
j  or  -^p  are  called  whole  tones;  intervals  having  the  ratios  -|-| 
are  called  /iaZ/  iones.  It  will  be  noted  that  in  the  above  scale 
there  are  five  whole  tones  and  two  half  tones  in  the  octave 
from  C  to  C'. 

The  scale  may  be  extended  above  or  below  the  octave  given 
in  Fig.  404  by  using  the  ratios  f ,  *,  |,  etc.  An  octave  above 
C',  that  is,  C",  will  have  1024  vibrations;  an,  octave  below  C, 
128  vibrations. 

The  minor  diatonic  scale  consists  of  eight  notes  similar  in 
letter  and  name  to  those  of  the  major  scale,  but  having  ratios 
derived  from  the  minor  chord. 

447.  Key  Notes.  The  key  note  is  the  note  taken  as  do,  or 
1,  of  the  scale.  A  scale  having  C  as  the  key  note,  as  written 
above,  is  sometimes  called  the  natural  scale.  In  order  to 
accommodate  different  voices  and  instruments,  however,  it  is 


SOUND  295 

frequently  desirable  to  change  the  key  note  of  the  scale  from 
C  to  some  other  note,  as  for  example,  D,  F,  or  G.  In  order 
to  write  the  scale  in  any  key,  all  that  is  necessary  is  to  select 
the  vibration  number  corresponding  to  that  letter  and  multi- 
ply it  successively  by  the  fractions  f ,  f ,  f ,  f ,  {,  ^,  2,  and  so 
on.  For  example,  suppose  that  we  wish  to  write  the  scale  in 
the  key  of  D.  We  select  D  from  the  diatonic  scale  as  our  key 
note,  its  vibration  number  being  288.  To  get  E  we  multiply 
288  by  f  =  320;  in  a  similar  manner  F  =  288  X  f  =  360; 
G  =  288  X  1  =  384;  A  =  288  X  f  =  432;  B  =  288  X  f  =  480; 
C'  =  288  X  ~  =  540;  D'  =  288  X  2  -  576.  Now  having  C' 
we  may  obtain  C;  that  is,  C  =  J  of  540  =  270. 

Below  we  have  written  for  comparison  scales  in  the  key  of 
C,  D,  and  G. 


C 

D 

E 

F 

G 

A 

B 

C' 

Key 

of 

C 

256 

288 

320 

341 

384 

426 

480 

512 

Key 

of 

D 

270 

288 

324 

360 

384 

432 

480 

540 

Key 

of 

G 

256 

288 

320 

360 

384 

432 

480 

512 

448.  Standards  of  Pitch.     In  physics  we  assign  to  middle  C 
256  vibrations  per  second.     In  music,  however,  the  standard  of 
pitch  commonly  employed  is  that  which  assigns  to  A  4^5  vibra- 
tions per  second.     This  is  called  the  international  standard  of 
pitch  and  is  that  to  which  most  musical  instruments  are  tuned. 

449.  An  Octave  on  the  Piano.     The  keys  representing  an 
octave  on  the  piano  are  shown  in  Fig.  405,  there  being  eight 

white  and  five  black  keys.     The     __ 

black  keys  represent  notes  called 

sharps  and  flats.     A  sharp  is  a 
note  having  a  vibration  number 


\D\E    F\G\A\1 


higher  than  that  of  a  given  note;  FIG  495 

a  flat  is  a  note  having  a  vibration 

number  lower  than  the  given  note.     Thus,  the  first  black  key 

above  C  is  the  sharp  of  C  and  the  flat  of  D.     These  thirteen 

notes,  eight  white  and  five  black,  constitute  an  octave. 


296  HIGH  SCHOOL  PHYSICS 

In  order  to  produce  music  in  different  keys  on  instruments 
having  fixed  keyboards,  such  as  the  piano  and  organ,  it  is 
necessary  to  determine  upon  some  arbitrary  ratio  from  note  to 
note.  This  changing  the  ratios  of  the  diatonic  scale  to  those 
of  other  values  is  called  tempering.  In  fixing  the  ratios  from 
note  to  note  on  the  piano,  musicians  have  agreed  to  adopt  a 
system  known  as  equal  temperament;  that  is,  the  ratio  between 
all  notes  is  equal.  The  ratio  number  selected  as  being  most 
satisfactory  is  the  twelfth  root  of  2;  that  is,  1.05946.  Thus 
if  we  fix  the  value  of  A  as  that  of  standard  pitch,  namely,  435 
vibrations  per  second,  then  the  sharp  of  A,  the  next  black  key 
above  it,  will  be  435  X  1.05946  =  460.9;  the  next  key,  B,  will 
be  460.9  X  1.05946  =  488.3,  and  so  on. 

450.  Tempered  Scale  of  Piano.  The  vibration  numbers 
for  the  thirteen  notes  on  a  piano,  from  C  to  C',  based  on 
A  as  435,  are  given  in  the  following  table.  The  notes  marked 
Xiy  Xzj  xs  Xtj  and  x-0  represent  the  five  black  keys  of  the  octave. 
C  =  258.7,  xi  =  274.1,  D  =  290.3,  x2  =  307.6,  E  =  325.9,  F 
=  345.3,  xz  =  365.8,  G  =  387.6,  z4  =  410.6,  A  =  435,  z5  = 
460.9,  B  =  488.3,  Cf  =  517.4.  A  tempered  scale  such  as  that 

/the  piano  is  sometimes  called  a  chromatic  scale. 
451.  Quality  of  Sound.  Sounds  may  differ  in  three  respects ; 
namely,  (a)  in  loudness,  (b)  in  pitch,  (c)  in  quality.  What  we 
mean  by  quality  or  timbre  may  be  illustrated  as  follows:  If 
middle  C,  for  example,  be  simultaneously  struck  on  a  piano, 
a  violin,  and  a  cornet,  the  pitch  is  the  same  in  all  three  cases; 
and  this  may  likewise  be  true  of  the  loudness  of  the  three  sounds. 
We  would  have  no  hesitation,  however,  in  assigning  one  sound 
to  the  piano  as  its  source,  another  to  the  violin,  and  the  third 
to  the  cornet.  This  property  which  enables  us  to  assign  a 
musical  sound  to  a  definite  source  is  called  quality  or  timbre. 
The  quality  of  a  musical  sound  is  due  to  the  number  and  char- 
acter of  the  overtones  present  (Art.  453)  and  is  determined  by 
the  form  of  the  resulting  sound  wave. 


SOUND 


297 


VIBRATION  OF  STRINGS 

452.  Segmental  Vibration  of  Strings.     Experiment.  '  (a)    If 
one  end  of  a  long  flexible  rope  be  fastened  to  the  wall  and  the 
other  end  moved  up  and  down  by  the  hand  in  such  a  way 
that  the  rope  is  caused 

to  swing  as  a  whole,  in 

somewhat    the    same 

manner  as   when   used 

by    children   in   "  skip-  FIG.  406 

ping     rope,"     we     will 

have  an  example  of  a 

string    vibrating    in    a  FlG  4Q7 

single      segment,      Fig. 

406.     The  rope  does  not  vibrate  in  a  vertical  plane,  but  has  a 

somewhat   circular  motion;  this  is  true,  also,  of  all  vibrating 

strings.     If  now  the  hand  be  moved  more  rapidly,  the  rope 

may  be  made  to  break  up  into  two,  three,  or  more  segments, 

as  shown  in  Fig.  407,  depending  upon  the  rate  at  which  the 

impulses  are  imparted.     The  points  of  least  motion,  N  and  N, 

are  called  nodes;  the  points  of  greatest  motion,  A,  are  called 

antinodes. 

453.  Fundamental  and  Overtone.     Fig.  408  A  illustrates  a 
string  vibrating  in  a  single  segment.     In  this  condition  it  gives 

off    its    lowest    tone.     The 

fundamental  of  any  sound- 
ing body  is  the  tone  of  low- 
est pitch  which  the  body  is 
capable  of  giving. 

Fig.  408  B  illustrates  the 
string  vibrating  in  two  seg- 
ments. In  this  case  it  gives 


G 
FIG.  408 

off  its  first  overtone,  that  is, 

a  tone  an  octave  above  the  fundamental;   in  C  the  string  is 
represented  as  vibrating  in  four  segments,  giving  off  a  tone 


298  HIGH  SCHOOL  PHYSICS 

two  octaves  above  the  fundamental.     An  overtone  is  the  tone, 
ffiven  off  by  the  sounding  body  when  vibrating  in  parts. 

A  string  may  vibrate  as  a  whole  or  it  may  break  up  into 
segments,  as  shown  above.     Indeed  a  string  may  vibrate  as  a 


whole,  from  a  to  c,  and  in  parts  at  the  same  time,  Fig.  409. 
In  this  case  the  tone  given  off  is  a  combination  of  the  funda- 
mental and  the  overtones. 

454.  The  Sonometer.  The  sonometer  is  an  instrument  used 
in  studying  the  laws  of  vibration  of  strings.  It  is  a  hollow 
wooden  box  upon  which  is  stretched  a  number  of  strings.  A 
spring  balance  or  other  device  is  used  to  determine  the  stretch- 
ing force  acting  on  the  string  (Supplement,  581),  while  a  small 


FIG.  410 

wooden  "  bridge  "  is  employed  to  vary  its  length.  By  means 
of  an  instrument  similar  to  the  one  shown  in  Fig.  410  the 
following  laws  may  be  verified. 

455.  Laws  of  Vibration  of  Strings.  I.  The  pitch  of  a  string 
varies  inversely  as  its  length.  The  shorter  the  string  the  higher 
the  pitch.  For  example,  if  a  string  one  meter  long  gives  a 
pitch  due  to  100  vibrations  per  second,  then  the  same  string 
half  a  meter  in  length,  the  stretching  force  being  constant, 
will  give  a  pitch  an  octave  higher  than  the  first ;  that  is,  a  pitch 
due  to  200  vibrations  per  second. 

II.  The  pitch  of  a  string  varies  directly  as  the  square  root  of 
the  stretching  force.  If  a  string  stretched  by  a  force  of  one  kilo- 


SOUND  299 

gram  make  100  vibrations  per  second,  then  the  same  string 
stretched  by  a  force  of  4  kilograms  will  make  200  vibrations  per 
second;  that  is,  100:  200  =  \/l:  -\/4. 

III.  The  pitch  of  a  string  varies  inversely  as  the  square  root  of 
the  mass  per  unit  of  length.  Thus  for  a  given  length  and  stretch- 
ing force,  the  lighter  the  string  the  higher  will  be  its  pitch. 

VIBRATION  OF  AIR  IN  PIPES 

456.  Vibration    in    Pipes.     Musical    instruments    may    be 
divided  into  two  great  classes:    (a)  stringed  instruments  and 
(b)  wind  instruments.     The  notes  which  are  produced  by  wind 
instruments  are  due  to  the  vibration  of  air  columns  within 
them.     We  commonly  speak  of  a  wind  instrument  as  a  pipe. 

The  various  kinols  of  wind  instruments  differ  chiefly  in  the 
mode  of  excitation  of  vibration  of  the  enclosed  column  of  air. 
The  part  of  the  instrument  in  which  the  vibrations  are  excited 
is  called  the  mouthpiece.  Mouthpieces  are  of  three  types: 
(a)  Those  in  which  the  air  is  blown  across  a  sharp  edge  or 
across  an  opening,  as  in  the  flute  or  organ  pipe.  This  form  of 
excitation  may  be  illustrated  by  blowing  across  the  mouth  of  a 
small  bottle,  or  better  still,  a  discharged  cartridge  shell.  A  com- 
mon tin  whistle  illustrates  fairly  well  the  principle  of  construc- 
tion of  the  organ  pipe,  (b)  Those  in  which  the  air  is  forced 
through  an  opening  which  is  partly  closed  by  an  elastic  tongue 
or  reed,  as  in  the  cabinet  organ,  the  accordion,  etc.  An  excel- 
lent illustration  of  the  reed  instrument  is  that  furnished  by 
the  common  "  mouth  organ,"  or  harmonica,  (c)  Those  in 
which  the  air  is  forced  through  a  slit,  formed  by  two  elastic 
membranes,  as  in  the  case  of  the  vibration  of  the  air  as  it  is 
forced  between  the  lips  in  playing  the  cornet,  or  the  vibration 
of  the  vocal  chords  in  the  production  of  voice. 

457.  Open  and  Closed  Pipes.     An  open  pipe  is  one  that  is 
open  or  free  at  both  ends.     In  Fig.  411  there  is  shown  an  open 
organ  pipe;    at  one  end  there  is  an  open  mouthpiece,  at  the 
other  an  open  or  free  passage. 


300 


HIGH   SCHOOL  PHYSICS 


In  Fig.  412  we  have  a  closed  organ  pipe.  There  is  at  one  end 
an  open  mouthpiece,  similar  to  that  of  the  open  pipe;  the 
other  end,  however,  is  closed. 

In  Fig.  413  there  is  shown  a  set  of  four  open  organ 
pipes,  which  when  sounding  their  fundamentals  pro- 
duce a  major  chord;  that  is,  they  sound  the  notes  do, 
mi,  sol,  do' . 

458.  Laws  of  Pipes. 
I.  The  pitch  of  a  pipe  va- 
ries inversely  as  its  length; 


1 


FIG.  411 


FIG.  412 


FIG.  413 


FIG.  414 


that  is,  the  shorter  the  pipe  the  higher  the  pitch.  Experiment. 
The  relation  of  the  length  of  a  pipe  to  its  pitch  may  be  strik- 
ingly demonstrated  by  using  a  pipe  into  one  end  of  which  is 
fitted  a  movable  piston,  Fig.  414.  If  the  piston  be  placed  at 
the  upper  end,  and  a  steady  stream  of  air  be  blown  into  the 
mouthpiece,  a  tone  having  a  definite  pitch  will  result.  If 
now  the  plunger  be  moved  downward  the  pitch  will  rise, 
becoming  very  shrill  as  the  plunger  approaches  the  mouthpiece. 
By  a  single  downward  and  upward  motion  of  the  piston,  the 
pitch  may  be  made  to  rise  and  fall,  illustrating  the  rise  and 
fall  of  the  pitch  of  a  siren  whistle. 

II.   An  open  pipe  gives  a  pitch  an  octave  higher  than  that  of 


SOUND  301 

a  dosed  pipe  of  the  same  length.  Experiment.  Remove  the 
plunger  from  the  pipe  used  in  the  preceding  experiment.  We 
now  have  an  open  pipe  of  a  given  length.  By  blowing  gently 
into  the  mouthpiece,  the  pipe  will  give  forth  its  lowest  or  fun- 
damental tone.  If  the  hand  be  now  placed  over  the  lower  end 
of  the  pipe,  thus  converting  it  into  a  closed  pipe,  it  will  give 
forth  a  tone  one  octave  lower  than  that  given  by  the  open  pipe, 
provided  the  fundamental  in  each  case  is  produced. 

459.  Overtones  in  Pipes.     Experiment.     If  we  blow  gently 
upon  a  pipe,  it  will  give  forth  its  fundamental  tone.     If  now 
we  blow  more  vigorously  the  pipe  will  give  a  tone  an  octave 
higher,  that  is,   will  sound  its  first  overtone;    blowing  still 
harder,  it  is  possible  to  make  the  pipe  sound  other  and  higher 
overtones. 

An  open  pipe  is  capable  of  giving  a  complete  series  of  over-  • 
tones,  having  frequencies  2,  3,  4,  5,  etc.,  times  that  of  the  1 
fundamental. 

A  closed  pipe  is  capable  of  giving  only  those  overtones  whose 
frequencies  are  3,  5,  7,  etc.,  times  that  of  the  fundamental. 

460.  Nodes  and  Antinodes  in  Pipes.     We  have  learned  that 
a  pipe  may  be  made  to  give  forth  not  only  its  fundamental  tone 
but  also  a  series  of  overtones.     What  happens  in  the  pipe  in 
the  case  of  the  production  of  overtones  is  somewhat  analogous 
to  that  which  occurs  in  a  string  when  it  breaks  up  into  segments 
and  gives  off  its  overtones.     The  air  column  within  the  pipe 
may  be  made  to  break  up  into  segments  forming  nodes  and 
antinodes. 

We  have  said  that  a  node  in  a  pipe  is  somewhat  similar 
to  that  in  a  string.  A  node  in  a  pipe,  however,  differs  from  a 
node  in  a  string  in  one  very  important  particular.  A  node  in  a 
string  is  a  point  of  least  motion.  A  node  in  a  pipe  is  a  point 
of  least  motion  and  of  greatest  changes  of  pressure.  (Supple- 
ment, 582.) 

When  an  open  pipe  is  sounding  its  fundamental  there  is  a 
node  at  the  middle  and  an  antinode  at  each  end,  Fig.  415. 


302 


HIGH  SCHOOL  PHYSICS 


There  is  always  an  antinode  at  the  open  end  of  a  pipe  when 
it  is  sounding  a  note. 

When  a  closed  pipe  is  sounding  its  fundamental  there  is  a 
node  at  the  closed  end  and  an  antinode  at  the  open  end,  Fig. 

416.  In  a  closed  pipe  there  is  always  a 
node  at  the  closed  end,  that  is,  a  point  of 
least  disturbance  of  the  air,  and  an  anti- 
node  at  the  open  end,  whether  the  pipe  be 
sounding   its   fundamental  or  one   of  its 

y      i    '          overtones. 

The  presence  of  nodes  in  pipes  may  be 
determined  experimentally  by  lowering  into 
the  pipe  a  small    paper  disc        ^- 
upon  which   has  been  placed 
FIG.  415    FIG.' 416    a  few  grains  of  fine  sand,  Fig. 

417.  When  the  disc  reaches 
a  node  (point  of  least  disturbance)  the  sand  is 
undisturbed;  when  the  disc  reaches  an  antinode 
(point  of  greatest  disturbance)  the  sand  is  vio- 
lently agitated. 

ORGANS  OF  VOICE  AND  HEARING 

461.  The  Vocal  Organs.  In  the  upper  portion 
of  the  throat  is  a  hard  projecting  mass  commonly 
called  "  Adam's  apple,"  which  constitutes  a  part 
of  the  larynx,  a  box-like  chamber  formed  of  car- 
tilages. The  larynx  is  the  primary  organ  of 
speech  and  song,  and  is  of  all  musical  instru- 
ments the  most  wonderful,  both  on  account  of 
its  simplicity  as  well  as  for  its  extreme  delicacy 
of  range.  Across  the  upper  end  of  the  larynx 
there  are  stretched  two  muscular  membranes, 
called  the  vocal  chords.  In  Fig.  418  the  vocal 
chords,  cc,  are  shown  as  they  would  appear  if  we  were  look- 
ing down  upon  them.  Between  the  edges  of  the  vocal  chords 


>3 

L 

\ 

FIG.  417 


SOUND 


303 


FIG.  418 
Vocal  Chords 


there  is  an  opening  called  the  glottis.  When  the  air  is  forced 
through  the  glottis,  the  vocal  chords  are  thrown  into  vibra- 
tion, which  gives  rise  to  the  tones  characteristic  of  the  human 
voice.  The  vocal  chords  are  controlled  by 
muscles.  When  the  edges  of  the  chords  are 
brought  close  together,  that  is,  when  the 
glottis  is  small,  the  vibration  rate  is  high, 
hence  the  pitch  of  the  voice  is  high;  when 
the  glottis  is  large  the  vibration  rate  is 
low,  hence  the  tone  is  low.  A  longitudinal 
section  of  the  larynx  is  shown  in  Fig.  419, 
cc  representing  the  vo- 
cal chords.  Just  above 
the  true  vocal  chords  are  two  folds  of 
mucous  membrane,  //,  called  the  false 
vocal  chords. 

462.  Range  and  Quality  of  the  Human 
Voice.  .The  vibration  range  of  the  ordi- 
nary piano  is  a  trifle  over  seven  octaves, 
the  lowest  note  being  that  of  about  27 
vibrations  per  second,  the  highest  some- 
what above  4000,  which  is  four  octaves 
above  middle  C.  The  range  of  the  human  voice  is,  for  the  or- 
dinary individual,  about  two  octaves.  The  trained  voice  of  the 
singer  frequently  has  a  range  somewhat  above  two  octaves. 
The  lowest  note  which  a  bass  voice  can  reach  is  about  two 
octaves  below  middle  C,  or  about  64  vibrations  per  second. 
The  highest  note  which  a  soprano  voice  can  reach  is  about  two 
octaves  above  middle  C;  that  is,  about  1040  vibrations  per 
second.  The  pitch  of  a  woman's  voice  is,  in  general,  about 
twice  as  high  as  that  of  a  man's  voice.  It  must  be  noted,  how- 
ever, that  the  range  of  each  is  practically  the  same;  namely, 
about  two  octaves. 

The  quality  of  the  human  voice  is  modified  by  the  resonance 
cavities  of  the  mouth  and  the  nasal  passage.     If  the  nostrils 


FIG.  419 
Section  of  Larynx 


304 


HIGH   SCHOOL  PHYSICS 


be  closed  by  the  fingers  and  we  attempt  to  recite  the  words 
:<  The  moon  is  beaming,"  we  will  have  strikingly  illustrated 
the  effects  of  changing  the  resonant  properties  of  the  nasal 
cavity. 

463.  The  Organs  of  Hearing.     The  human  ear  consists  of 
three  parts  or  divisions:  (a)  the  external  ear,  (b)  the  middle 

ear,  and  (c)  the  internal 
ear,  Fig.  420.  The  ex- 
ternal ear  includes  the 
concha  and  the  tube  or 
canal  terminating  in  a 
thin  membrane  called  the 
drum  membrane  or  tym- 
panum T.  The  middle 
ear  contains  a  chain  of 
little  bones,  the  function 
of  which  is  to  transmit 
vibrations  from  the  tym- 
panum to  the  internal 
ear.  The  middle  ear 

communicates  with  the  mouth  chamber  by  means  of  a  tube 
called  the  Eustachian  tube  E,  the  function  of  which  is  to  equal- 
ize the  pressure  between  the  air  in  the  middle  ear  and  that  on 
the  outside.  The  internal  ear  is  placed  deep  in  the  skull  and 
consists  of  three  parts:  (a)  the  vestibule  V,  (b)  the  semicircu- 
lar canals  S,  three  in  number,  and  (c)  the  cochlea,  or  snail  shell 
C,  all  of  which  are  filled  with  a  watery  fluid.  In  this  watery 
fluid  of  the  internal  ear  we  find  the  nerve  fibers,  which  spread 
out  from  the  auditory  nerve. 

464.  How  we  Hear.      The  process  of  hearing  begins  with 
the  transmission  of  sound  waves  to  the  drum  of  the  ear.     These 
vibrations,  it  will  be  remembered,  consist  of  condensations  and 
rarefactions  which  produce  upon  the  drum  membrane  changes 
of  pressure,  causing  it  to  vibrate  back  and  forth.     The  vibra- 
tions are  then  transmitted  by  the  ossicles  of  the  middle  ear 


FIG.  420.  —  Mechanism  of  the  Ear 


SOUND  305 

to  the  fluids  of  the  internal  ear,  whence  it  is  transmitted  to 
the  fibers  of  the  auditory  nerve.  This  disturbance  of  the  end 
organs  of  the  auditory  nerve  produces  a  nervous  impulse  which 
travels  to  the  brain  and  there  gives  rise  to  the  sensation  of 
hearing. 

465.  Limits  of  Audibility.    The  human  ear  is  capable  of  hear- 
ing sounds  covering  a  range  of  about  ten  octaves.     The  limits 
of  audibility  vary  in  a  marked  degree  for  different  individuals. 
Some  exceptional  ears  can  probably  hear  as  high  as  40,000  or 
50,000  vibrations  per  second.      The  ordinary  limits,  however, 
lie  between  30  and  30,000  vibrations  per  second.      This  means 
that  there  is  a  large  range  of  vibration  the  pitch  of  which  is 
either  too  Low  or  too  high  to  be  heard. 

466.  The  Phonograph.     The  phonograph  is  closely  allied  to 
the  organs  of  human  speech  and  hearing  so  far  as  simplicity  of 
construction  and  perfection  of  execution  are  concerned.     This 
instrument  consists  of  a  mouthpiece  across  one  end  of  which 
there  is  stretched  a  vibrating  disc,  to  the  center  of  which  is 
attached  a  needle.     This  part  of  the  apparatus  resembles  some- 
what the  external  ear  and  the  tympanic  membrane.     The  needle 
attached  to  the  disc  corresponds  somewhat  'in  its  working  to 
the  bones  connecting  the  drum  of  the  ear  with  the  internal  ear. 
When  it  is  desired  to  prepare  a  record  the  mouthpiece  is  ad- 
justed so  that  the  needle,  communicating  with  the  center  of 
the  disc,  rests  lightly  upon  a  cylinder  of  some  soft  substance, 
such  as  wax.     A  person  speaking  or  singing  into  the  instru- 
ment causes  the  disc  to  vibrate,  which  in  turn  causes  the  needle 
to  trace  out  in  the  soft  wax,  which  is  in  motion,  a  series  of  tiny 
pits  or  holes  of  irregular  depth.     Now  if  the  wax  be  allowed  to 
harden  and  the  cylinder  be  moved  uniformly  under  the  needle, 
the  latter  will  vibrate  in  unison  with  the  irregular  depressions 
contained  in  its  surface.     This  motion  of  the  needle  causes  a 
vibration  of  the  disc  in  the  mouthpiece  or  horn  of  the  instru- 
ment, which  in  turn  sets  the  air  in  vibration,  producing  the 
characteristic  tones  of  the  phonograph. 


306  HIGH  SCHOOL  PHYSICS 

The  quality  of  tone  given  by  a  phonograph  depends  upon 
the  nature  of  the  needle  used,  that  is,  whether  it  be  of  metal 
or  wood,  and  upon  the  resonating  quality  of  the  framework  of 
the  instrument. 

EXERCISES  AND  PROBLEMS  FOR  REVIEW 

1.  Define:  Sound,  acoustics,  transverse  wave,  longitudinal  wave. 

2.  Make  drawing  to  illustrate  wave  length  and  amplitude  in    (a) 
transverse  wave;  (b)  longitudinal  wave. 

3.  Compare  the  motion  of  the  wave  with  the  motion  of  the  vibrating 
particle  in  the  case  of  (a)  a  surface  water  wave;    (b)  a  wave  passing  over 
a  field  of  grain. 

4.  Explain  the  meaning  of  the  following  equation,  and  define  each 
term,  v  =  \/e/d. 

5.  Why  does  the  timer  in  a  200  yard  dash  start  his  stop  watch  by 
the  flash  of  the  pistol  rather  than  by  its  report? 

6.  Explain  why  an  increase  in  temperature  causes  an  increase  in  the 
velocity  of  sound  in  air. 

7.  What  is  the  velocity  of  sound  in  air,  in  feet,  at  (a)  0°  C.?   (b)  -  20° 
C.?  (c)  +  20°  C.? 

8.  What  is  the  approximate  relation  of  the  velocity  of  sound  in  air, 
water,  iron? 

9.  Explain  why  the  velocity  of  sound  in  metals  is  greater  than  that 
in  air. 

10.  A  flash  of   lightning  is  seen  and  5  seconds  later  the  thunder  is 
heard.     How  far  away  is  the  lightning  discharge,  the  temperature  being 
25°  C.? 

11.  A  sunset  gun  was  fired  at  exactly  6.30  P.M.  at  a  fort.     What  time 
was  it  when  the  sound  was  heard  20  miles  away,  the  temperature  being 
20°  C.? 

12.  What  is  the  distinction  between  loudness  and  intensity?     Upon 
what  four  factors  does  the  intensity  of  sound  depend? 

13.  Explain  why  striking  a  bell  a  vigorous  blow  causes  it  to  give  off  a 
louder  sound  than  if  it  be  tapped  lightly. 

14.  Compare  the  intensity  of  a  given  sound  at  two  points,  one  a  half 
mile  from  the  source,  the  other  three  miles  from  the  source. 

15.  Explain  resonance  and  give  an  example. 

16.  Give  the  meaning  of  the  following  equation,  and  explain  how  it  is 
derived,  I  =  v/n, 

17.  A  closed  resonance  tube  2  ft.  in  length  responds  to  a  given  fork 
when  the  temperature  is  25°  C.     Find  the  frequency  of  the  fork. 


SOUND  307 

18.  A  closed  resonance  tube  18  in.  in  length  responds  to  a  fork  which 
makes  320  vibrations.     Find  the  temperature. 

19.  A  closed  organ  pipe  is  3  ft.  long,     (a)  What  is  the  wave  length  of 
its  fundamental  tone?     (b)  How  long  must  an  open  pipe  be  to  give  the 
same  tone? 

20.  Define  and  give  illustration  of  beats. 

21.  Make  drawing  to  illustrate  the  effect  of  two  sound  waves  upon  each 
other  such  that  they  produce  (a)  a  louder  sound;   (b)  silence;   (c)  beats. 

22.  Define  pitch,  and  explain  how  a  siren  may  be  used  to  determine 
the  pitch  of  a  sounding  body. 

23.  A  current  of  air  was  blown  against  the  disc  of  a  siren  having  a 
row  of  30  holes,  while  the  disc  was  making  200  revolutions  per  second. 

(a)  What  was  the  pitch  of  the  resulting  tone?    (b)  If  the  speed  of  the  siren 
were  doubled,  how  would  the  pitch  be  effected? 

24.  A  whistle  in  sounding  makes  a  certain  number  of  vibrations  per 
second,  which  strike  the  ear  of  a  person  who  is  standing  still.     Suppose 
now  that  the  person  walk  toward  the  whistle.     Will  the  number  of  vibra- 
tions falling  upon  his  ear  per  second  be  increased  or  diminished?     How 
will  it  effect  the  pitch?     How  do  you  account  for  the  rise  of  the  pitch  of  a 
locomotive  whistle  which  is  rapidly  approaching? 

25.  Define:  Music,  musical  interval,  octave,  major  triad,  major  chord. 

26.  The  tones  of  three  forks  form  a  major  triad.     The  middle  fork 
gives  a  note  of  330  vibrations  per  second.     Find  the  vibration  rate  of  the 
other  two  forks. 

27.  Define  diatonic  scale.     Name  in  order  the  eight  notes  of  which  it 
is  composed. 

28.  How  many  notes  per  octave  are  there  in  the  chromatic  scale  of 
the  piano?     W'hat  do  the  black  keys  represent? 

29.  What  is  the  ratio  from  one  key  to  the  next  on  the  piano?     What 
name  is  given  to  a  system  of  tempering  in  which  the  ratios  are  all  equal? 

30.  Which  offers  the  greater  possibilities  to  the  musician,  (a)  the  piano  or 
the  violin?  (b)  the  cornet  or  the  trombone?    Give  reasons  for  your  answers. 

31.  Make  drawing  to  illustrate  nodes  and  antinodes  in  the  case  of  the 
vibration  of  strings. 

32.  Define  fundamental  tone,  overtone.     When  a  string  vibrates  both 
as  a  whole  and  in  parts  at  the  same  time,  what  can  you  say  of  the  character 
of  the  tone  given  off? 

33.  In  what  three  ways  may  sounds  differ?     Define  and  illustrate 
quality  of  sound. 

34.  State  the  laws  of  vibration  of  strings. 

35.  How  will  the  pitch  of  a  string  be  affected  (a)  if  its  length  be  doubled? 

(b)  if  its  tension  be  quadrupled?   (c)  if  the  mass  be  increased  nine  times? 


308  HIGH   SCHOOL  PHYSICS 

36.  A  given  string  acted  upon  by  a  force  of  1  Ib.  makes  200  vibrations 
per  second.     What  will  be  the  frequency  of  the  string  if  the  stretching  force 
be  increased  to  4  Ibs.? 

37.  In  playing  the  violin  the  musician  moves  the  fingers  of  his  left  hand 
back  and  forth  along  the  string.     Explain  what  effect  this  has  on  the  pitch. 

38.  What  is  the  relation  of  the  length  of  a  pipe  to  its  pitch?     What  is 
the  relation  of  the  pitch  of  an  open  pipe  to  that  of  a  closed  pipe?    An  open 
pipe  of  given  length  is  sounding  its  fundamental.     Suppose  that  a  person 
stop  one  end  by  means  of  a  card.     How  will  the  pitch  be  affected? 

39.  Define  node  in  a  pipe,  and  tell  wherein  it  differs  from  a  node  in  a 
string. 

40.  How  may  the  presence  of  nodes  in  pipes  be  determined  experi- 
mentally? 

41.  When  a  closed  pipe  is  emitting  a  note  what  always  occurs  at 
(a)  the  closed  end?  (b)  the  open  end? 

42.  Make  drawing  to  illustrate  the  position  of  the  node  within  (a)  an 
open  pipe;  (b)  a  closed  pipe,  when  each  is  sounding  its  fundamental. 

43.  Make  sketch  and  describe  briefly  the  vocal  organs.     Explain  the 
condition  of  the  chords  when  the  pitch  of  the  voice  is  (a)  high;   (b)  low. 

44.  Make  sketch  of  the  ear,  and  describe  how  changes  of  pressure  due 
to  condensations  and  rarefactions  of  sound  waves  are  transmitted  from  the 
external  to  the  internal  ear.     Describe  the  Eustachian  tube,  and  explain 
briefly  its  function. 

For  additional  Exercises  and  Problems,  see  Supplement,  583 
and  584. 


CHAPTER  XI 
LIGHT 

NATURE  OF  LIGHT 

467.  Definitions.     A  luminous  body  is  one  which  emits  light. 
The  sun  and  the    stars  are   luminous  bodies;    so,  too,  is  a 
candle  flame  or  the  glowing  filament  of  an  incandescent  lamp. 
Bodies  which  shine  by  light  other  than  their  own  are  called 
illuminated   bodies.       The  moon  is  a  good  illustration  of  an 
illuminated  body. 

A  transparent  body  is  one  which  allows  light  to  pass  through 
it  readily;  that  is,  it  is  one  which  we  can  see  through,  as,  for 
example,  window  glass.  A  translucent  body  is  one  which  allows 
only  a  part  of  the  light  to  pass  through,  without  permitting 
objects  to  be  distinctly  seen,  as  in  the  case  of  "  frosted  "  glass. 
An  opaque  body  is  one  which  does  not  allow  light  to  pass 
through  it.  It  must  be  noted  in  this  connection  that  the  terms 
transparent,  translucent,  and  opaque  are  used  in  a  purely  rela- 
tive sense.  Wood,  for  example,  is  opaque,  yet  a  shaving  from 
a  pine  board  may  be  obtained  so  thin  as  to  be  almost  trans- 
parent. Gold  may  be  beaten  out  into  sheets  so  thin  as  to  be 
translucent. 

Optics  is  that  branch  of  physics  which  treats  of  light. 

468.  The  Sun  a  Source  of  Energy.     The  sun  is  not  only  the 
most  familiar  source  of  light,  but  it  is  also  the  earth's  chief 
source  of  energy.     All  the  energy  of  plant  and  animal  life  is 
directly  traceable  to  the  sun,  as  is  also  the  energy  furnished 
by  wind  and  water  power.     The  energy  of  our  coal  fields,  too, 
is  nothing  more  than  the  stored-up  energy  of  the  sun's  rays  of 
by-gone  ages.     Now  the  sun  is  some  93,000,000  miles  from  the 
earth,  and  the  question  may  be  asked:  How  does  this  energy 


310  HIGH   SCHOOL   PHYSICS 

get  to  the  earth  across  the  enormous  gulf  of  intervening  space? 
Two  theories  have  been  advanced  to  explain  the  transmission 
of  the  sun's  energy;  namely,  (a)  the  emission  theory  and  (b)  the 
wave  theory. 

The  emission  or  corpuscular  theory,  which  was  advocated  by 
Sir  Isaac  Newton,  assumed  that  the  energy  of  the  sun  is  carried 
through  space  by  tiny  particles  or  corpuscles  which  are  shot  off 
from  that  body  with  an  enormous  velocity,  and  which  carry 
energy  somewhat  as  a  bullet  carries  energy  from  a  gun.  This 
theory  is  no  longer  held  by  scientific  men. 

The  undulatory  or  wave  theory,  which  was  first  definitely 
stated  by  Huygens,  a  Dutch  physicist,  in  1678,  and  which  is 
now  generally  accepted,  assumes  that  the  energy  of  the  sun 
is  transmitted  through  space  by  means  of  waves,  through  a 
medium  called  the  ether. 

469.  The  Ether.     The  ether  is  supposed  to  be  a  medium 
which  fills  all  space,  not  only  between  the  heavenly  bodies, 
but  also  between  the  molecules  of  matter  itself,  and   which 
is    capable    of    transmitting   energy.      It   seems   to   offer  no 
Resistance  to  the  passage  of  bodies  through  it,  since  in  all  the 
centuries  in  which  astronomers  have  been  making  accurate 
observations  of  the  heavenly  bodies  no  retardation  has  ever 
been  observed.     No  one  has  even  seen  the  ether  or  felt  it  or 
weighed  it;  nevertheless  it  is  convenient  to  assume  that  such 
a  medium  does  exist  in  order  to  explain  the  phenomena  of  light, 
radiant  energy,  and  electricity.     (Supplement,  598.) 

470.  The  Wave  Theory  of  Light.     This  theory,  to  repeat, 
assumes  that  the  energy  of  the  sun  and  other  luminous  bodies 
is  transmitted  through  space  by  means  of  waves.     Now  only  a 
part  of  the  energy  that  comes  -to  us  from  the  sun  in  the  form  of 
ether  waves  appears  as  light;    indeed,  ether  waves  from  the 
sun  may  be  divided  into  three  classes:    (a)  long  ether  waves 
which  give  rise  to  heat,  and  which  are  sometimes  known  as 
"  radiant  heat";    (b)  short  ether  waves  which  are  known  as 
light  waves;   and  (c)  very  short  ether  waves  which  give   rise 


LIGHT 


to  chemical  reactions,  such,  for  example,  as  those  which  affect 
a  photographic  plate.  Only  those  waves  which  affect  the  eye 
are  called  light  waves. 

Light  may  be  defined  as  that  vibration  of  the  ether  which  is 
capable  of  affecting  the  organs  of  sight. 

471.  Comparison  of  Light  Waves  with  Sound  Waves.     Light 
waves  differ  from  sound  waves  in  several  very  important  par- 
ticulars:    (a)  Sound  waves  occur  in  matter;  light  waves  in 
ether,    (b)  Sound  waves  in  fluids  are  longitudinal;  light  waves 
are  always  transverse,  (c)  Sound  cannot  be  transmitted  through 
a  vacuum;    light  is  readily  transmitted  through  a  vacuum, 
(d)  Sound  waves  are  comparatively  long,   the  wave  length 
corresponding  to  middle  C  being  about  130  centimeters;  light 
waves    are   very  short,    that    of   yellow    light    being    about 
0.0000589  centimeter,    (e)  The  speed  of  sound  waves  is  insigni- 
ficant as  compared  with  that  of  light.     It  has  been  found  that 
light  waves  travel  with  a  velocity  nearly  a  million  times  as 
great  as  that  of  sound  waves  in  air. 

472.  Ray,  Beam,  and  Pencil.     Since  light  is  transmitted  by 
means  of  waves  its  propagation  through  space  may  be  repre- 
sented by  means  of  a  series  of  concen- 
tric circles,  as  shown  in  Fig.  421,  in 

which  L  is  the  source  of  light,  the 
waves  traveling  outward  in  all  direc- 
tions. The  line  LA  shows  the  direc- 
tion of  motion  of  a  given  set  of  wave 
fronts  and  is  called  a  ray.  A  ray  is  a 
line  drawn  to  represent  the  direction 
of  propagation  of  a  wave  of  light.  A 
beam  of  light  is  a  number  of  parallel  rays,  Fig.  422.  A  pencil 


FIG.  422 


FIG.  423 


312 


HIGH   SCHOOL   PHYSICS 


of  light  is  a  number  of  rays  passing  through  a  common  point 
called  the  focus.  Fig.  423  illustrates  convergent  and  divergent 
pencils.  The  wave  front  is  represented  in  each  case  by  the 
line  ab. 

473.  Propagation  of  Light.  Light  travels  in  straight  lines, 
provided  the  medium  through  which  it  is  propagated  is  homo- 
geneous, that  is,  a  medium  having  the  same  density  and  elas- 
ticity throughout.  The  fact  that  light  is  propagated  in  straight 


FIG.  424 

lines  is  seen  when  a  beam  is  passed  into  a  darkened  room 
in  which  there  are  particles  of  dust  floating  in  the  air.  The 
marksman  in  sighting  his  gun,  the  surveyor  in  adjusting  his 
instruments,  and  the  mechanic  in  much  of  his  work,  all  take 
account  of  this  fundamental  property  of  light;  namely,  that  it 
travels  in  straight  lines,  Fig.  424. 

474.    Shadows.     If  an  opaque  object  be  held  in  front  of  a 
luminous  body  there  appears  in  the  rear  of  the  opaque  body  a 


FIG.  425 


dark  space  called  a  shadow,  which  has  three  dimensions:  length, 
breadth,  and  thickness.     That  portion  which  appears  on  the 


LIGHT 


313 


wall  or  screen  is  called  a  section  of  the  shadow.  A  shadow  may 
consist  of  two  parts,  the  umbra  and  the  penumbra.  Fig.  425 
shows  the  umbra  and  penumbra  of  the  shadow  cast  by  the 
earth.  In  an  eclipse  of  the  moon  this  body  passes  through  the 
cone  of  the  earth's  shadow,  entering  the  penumbra  first  and 
leaving  it  last. 

475.  The  Velocity  of  Light.  For  a  long  time  it  was  thought 
that  light  was  transmitted  through  space  instantaneously.  In 
1675  however,  Roemer,  a  young  Danish  astronomer,  who  was 
making  observations  at  the  observatory  at  Paris,  determined 
the  velocity  of  light  from  a  study  of  the  satellites  or  moons  of 
Jupiter.  This  planet  has  several  moons  which  revolve  about 
it  as  our  moon  does 
about  the  earth.  The 
inner  one  of  these  sat- 
ellites passes  into  the 
shadow  cast  by  Jupi- 
ter, Fig.  426;  that  is, 
it  is  eclipsed  once  on 
an  average  every  42 
hours,  28  minutes,  36 
seconds.  Roemer  cal- 
culated in  advance  the 
exact  time  that  each 

eclipse  should  occur  for  a  number  of  positions  of  the  earth  in  its 
orbit.  He  took  a  series  of  observations  as  the  earth  moved 
from  E  away  from  Jupiter  and  found  the  eclipses  occurred  at 
regularly  increasing  intervals  later  than  those  which  he  had 
computed.  When  the  earth  had  reached  the  point  Ef,  directly 
across  its  orbit  from  Jupiter,  the  eclipse  occurred  about  1000 
seconds  later  than  the  computed  time.  He  concluded  that  this 
apparent  delay  in  the  time  of  the  eclipse  was  due  to  the  time 
required  for  light  to  travel  across  the  earth's  orbit  a  distance 
of  about  186,000,000  miles.  Now  186,000,000/1000  =  186,000  : 
that  is  to  say,  the  velocity  of  light  is  186,000  miles  per  second. 


FIG.  426 


314 


HIGH   SCHOOL   PHYSICS 


Roemer's  wonderful  discovery  was  received  with  but  little 
favor  by  scientific  men,  and  indeed  was  practically  disregarded 
for  over  fifty  years  until  other  methods  were  discovered  for 
measuring  the  velocity  of  light. 

476.  The  Velocity  of  Light  in  Different  Media.     According  to 
Newton's  corpuscular  theory,  light  should  travel  faster  in  a 
dense  medium,  such  as  water  or  glass,  than  in  a  rare  medium; 
according  to  the  wave  theory,  on  the  other  hand,  light  should 
have  the  greater  velocity  in  a  rare  medium.     Therefore,  when 
in  1850  Foucault,  a  French  physicist,  measured,  by  means  of 
a  rotating  mirror,  the  velocity  of  light  in  air  and  in  water, 
and  found  thereby  that  the  speed  of  light  is  greater  in  air  than 
in  water,  he  thus  established  on  a  firm  basis  the  undulatory 
or  wave  theory,  which  is  now  generally  accepted. 

The  velocity  of  light  is  greater  in  a  vacuum  than  in  air,  and 
is  greater  in  air  than  in  water  or  glass. 

INTENSITY  OF  LIGHT 

477.  Images  Formed  through  Small  Apertures.     If  a  candle 
or  other  luminous  body  be  placed  in  front  of  a  small  aperture 


FIG.  427 

in  an  opaque  screen,  Fig.  427,  there  will  be  formed  upon  a 
second  screen  S  an  inverted  image  of  the  body.  The  following 
points  with  respect  to  the  formation  of  images  through  aper- 
tures are  to  be  noted:  (a)  The  image  is  inverted  and  per- 
verted; that  is,  it  is  upside  down  with  respect  to  the  object 
and  the  right  side  of  the  image  corresponds  to  the  left  side  of 
the  object.  This  is  due  to  the  fact  that  rays  of  light  from  the 


LIGHT  315 

different  points  of  the  object  pictured  on  the  screen  cross  as 
they  pass  through  the  aperture,  (b)  The  size  of  the  image 
depends  on  the  distance  of  the  screen  from  the  aperture,  (c) 
The  smaller  the  opening  the  less  the  illumination  of  the  image 
but  the  greater  the  distinctness  of  outline;  on  the  other  hand, 
as  the  aperture  becomes  larger  the  illumination  of  the  image 


FIG.  428 

increases  but  its  distinctness  diminishes,  due  to  the  overlap- 
ping of  the  rays,  as  shown  in  Fig.  428. 

478.  The  Pinhole  Camera.  The  principle  of  the  formation 
of  images  through  small  apertures  is  made  use  of  in  the  employ- 
ment of  the  so-called  pi'nhole  camera  in  photography.  This 
apparatus  consists  of  a  small  box  painted  black  on  the  inside  to 


FIG.  429.  —  Pinhole  Camera 

prevent  undue  reflection  of  the  light  which  is  admitted  through 
a  small  aperture  or  "  pinhole."  The  photographic  film  is 
placed  in  the  rear  of  the  box  in  such  a  way  as  to  receive  the 
image  of  the  object  outside,  as  illustrated  in  Fig.  429.  A  camera 


316 


HIGH   SCHOOL  PHYSICS 


FIG.  430.  —  This  Picture  taken  by 
means  of  Pinhole  Camera 


of  this  type  is  very  inexpensive  and  may  be  employed  in  photo- 
graphing landscapes  and  other  scenes  where  long  exposures 

may  be  secured.  In  Fig.  430 
there  is  shown  a  picture  taken 
by  such  a  camera. 

479.  Intensity  of  Illumina- 
tion. By  intensity  of  illumi- 
nation we  mean  the  quantity 
of  light  per  unit  area.  Expe- 
rience teaches  us  that  the  far- 
ther one  is  away  from  a  given 
source  of  light  the  less  intense 
the  light  becomes.  This  is 
due  to  the  divergence  of  the 
rays,  as  shown  in  Fig.  431. 
Consider  screen  S  to  be  one  foot  from  L  and  screen  S'  to  be 
two  feet  from  the  source  of  light.  Now  the  quantity  of  light 
which  falls  upon  each  screen 
is  the  same.  The  rays  fall- 
ing on  S',  however,  are 
spread  out  over  four  times 
as  much  space  as  on  S', 
therefore  the  intensity  on 
a  unit  surface  of  S'  is  only 
one-fourth  as  great  as  that 
on  S.  This  is  an  illustration  of  the  law  of  inverse  squares, 
which  states  that  the  intensity  of  illumination  is  inversely  pro- 
portional  to  the'  square  of  the  distance  from  the  source.  This 
may  be  written 

intensity  at  S  :  intensity  at  Sf  =  d'2:  d2 

in  which  d  is  the  distance  of  screen  S  from  L,  and  d'  the  dis- 
tance of  S'  from  L. 


FIG.  431 


EXERCISES.    1.   How  does  the  quantity  of  light  on  screen  S  compare 
with  that  on  S'? 


LIGHT 


317 


2.  Suppose  that  S  is  2  ft.  from  L,  and  S'  4  ft.  How  does  the  intensity 
of  light  on  screen  S  compare  with  that  on  Sf  ?  How  will  the  intensities  on 
the  two  screens  compare  if  S'  be  placed  at  a  distance  of  3  ft.  from  L? 

480.  The  Photometer.  A  photometer  is  an  instrument  for 
measuring  the  intensity  of  light .  The  unit  of  intensity  is  the 
candle  power,  which  is  the  light  given  out  by  a  standard  candle. 
The  common  incandescent  electric  light  of  the  carbon  filament 
type  is  usually  of  16  candle  power. 

The  Bunsen  photometer,  Fig.  432,  consists  in  principle  of  a 
paper  screen  upon  which  there  is  a  small  circular  oil  or  grease 


FIG.  432 

spot.  If  the  paper  with  the  grease  spot  upon  it  be  held  up  to 
the  light,  in  front  of  an  open  window  for  example,  so  that  the 
paper  is  between  the  light  and  the  eye,  the  grease  spot  will 
appear  lighter  in  color  than  the  paper  because  it  is  more  trans- 
parent. Now  if  the  paper  be  held  up  in  front  of  a  dark  body, 
such  as  a  blackboard,  the  grease  spot  will  appear,  darker  than  the 
paper,  because  it  reflects  less  of  the  light  than  does  the  paper. 
When  the  intensity  of  illumination  on  both  sides  of  the  paper  is 
equal  the  distinction  between  the  grease  spot  and  the  paper  is 
reduced  to  a  minimum. 

To  determine  the  intensity  of  light  by  means  of  this  appa- 
ratus we  proceed  somewhat  as  follows:     A  standard  candle  is 


318  HIGH  SCHOOL  PHYSICS 

placed  at  a  given  distance  from  the  screen,  1  foot  say;  the  light, 
the  intensity  of  which  is  to  be  measured,  is  placed  on  the  other 
side  of  the  screen  and  then  moved  back  and  forth  until  a  posi- 
tion is  found  at  which  the  spot  on  the  screen  is  equally  illumi- 
nated from  both  sides.  From  the  law  of  inverse  squares  we  may 
now  determine  the  intensity  of  the  given  light  in  terms  of  its 
distance  from  the  screen.  If  the  candle  is  1  foot  from  the  screen 
and  the  light  4  feet  distant,  their  relative  intensities  are  as 
I2:  42,  that  is,  as  1 :  16.  Thus  we  say  that  the  intensity  of  the 
light  L  is  16  candle  power. 

EXERCISES.  3.  A  lamp  placed  3  ft.  from  a  screen  gives  an  illumination 
equal  to  that  of  a  standard  candle  placed  at  a  distance  of  1  ft.  from  the 
screen,  lamp  and  candle  being  on  opposite  sides.  Find  the  candle  power 
of  the  lamp. 

4.  A  gas  jet  and  an  electric  lamp  are  placed  on  opposite  sides  of  the 
screen  so  that  the  spot  upon  the  latter  is  equally  illuminated.     The  gas 
jet  is  2  ft.  from  the  screen;   the  electric  light  6  ft.     Compare  the  candle 
power  of  the  two  sources. 

5.  It  is  desired  to  find  the  candle  power  of  a  given  arc  light.     It  is 
found  that  when  a  standard  candle  is  placed  1  ft.  from  the  screen  of  the 
photometer  the  latter  has  to  be  removed  to  a  distance  of  30  ft.  from  the 
arc  light.     Find  the  candle  power  of  the  arc. 

REFLECTION 

481.   The  Law  of  Reflection.     If  a  beam  of  light  from  a 

source  A,  Fig.  433,  fall  upon 
a  polished  surface  it  will  be 
reflected  to  C.  The  line  BD 
is  drawn  perpendicular  to 
the  surface  of  the  mirror 
and  is  called  a  normal.  The 
angle  ABD,  formed  by  the 
incident  ray  and  the  nor- 
mal, is  called  the  angle  of 
incidence;  the  angle  DBC, 
formed  by  the  reflected  ray  and  the  normal,  is  the  angle  of 


LIGHT 


319 


M 


B 

FIG.  434 


reflection.     A  diagrammatic  representation  of  the  angle  of  in- 
cidence i,  and  the  angle  of  reflection  r,  is  that  of  Fig.  434. 

The  law:    The  angle  of  incidence  is 
'  *  equal  to  the  angle  of  reflection,  and  both 
lie  in  the  same  plane. 

482.  Mirrors  and  Images.  A  mirror 
is  any  polished  surface.  Images  formed 
by  mirrors  are  of  two  kinds,  real  and 
virtual.  Experiment,  (a)  If  a  candle 
be  held  between  the  center  of  curva- 
ture of  a  spherical  mirror  and  its  focus,  there  will  appear  on 
the  screen  a  real  image;  that  is,  an  image  formed  by  the 

actual  focusing  of  the  rays  of  light. 
Experiment,  (b)  If  now  the  candle 
be  placed  in  front  of  a  plane  mir- 
ror, a  virtual  image  will  be  formed 
and  will  appear  to  be  as  far  back  of 
the  mirror  as  the  candle  is  in  front 
of  it.  A  virtual  image  is  one  which 
appears  to  be  where  it  really  is  not. 
All  images  formed  in  plane  mirrors 
are  virtual  images. 

483.  Multiple  Images.  If  an  ob- 
ject such  as  a  candle  flame  or  a  gas 
flame  be  held  close  to  a  plate  glass 
mirror  and  viewed  at  an  angle,  a 
series  of  images  may  be  observed, 
Fig.  435,  the  second  being  the  bright- 
est one  of  the  series.  These  are 
called  multiple  images,  and  their  for- 
mation is  explained  by  the  fact  that 
the  light  from  the  object  is  reflected 
from  the  mirror  to  the  eye  from  both  surfaces,  as  shown  in 
Fig.  436.  The  first  and  rather  faint  image  which  appears  is 
due  to  the  reflection  from  the  surface  of  the  glass.  The  sec- 


FIG.  435 


wvv 

FIG.  436 


320 


HIGH   SCHOOL  PHYSICS 


ond  and  brightest  image  is  due  to  the  reflection  from  the  sil- 
vered rear  surface.  The  other  and  fainter  images  are  due  to 
secondary  reflections.  It  is  because  of  the  formation  of  multi- 
ple_images_that  glass  mirrors  cannot  be  successfully  used  in 
certain  kinds  of  spirnitifjf*  wnrk,  pu^h  as  astronomical  observa- 


tions. For  this  purpose  mirrors  made  of  highly  polished  metal, 
and  therefore  having  but  a  single  reflecting  surface,  are  used. 
484.  The  Formation  of  Images  in  Plane  Mirrors.  Given 
an  object  in  front  of  a  plane  mirror  to  find  the  position  and 
character  of  the  image.  Let  0,  Fig.  437,  be  an  object  in  front 
of  the  mirror.  Draw  from  this  point  two  rays  incident  upon 
the  mirror  at  m  and  m'  '.  Erect  the  normals  ma  and  m'b.  Now 


FIG.  437 


FIG.  438 


draw  the  line  mC  and  m'E  in  such  a  way  that  in  each  case  the 
angle  of  incidence  is  equal  to  the  angle  of  reflection.  Produce 
the  lines  Cm  and  Em'  until  they  meet  at  the  point  0'.  It  may 
be  shown  by  geometry  that  0'  lies  on  the  perpendicular  and  is 
as  far  back  of  the  mirror  as  0  is  in  front  of  it. 

Now  if  an  eye  be  placed  at  CE  it  will  receive  the  light  from 
the  object  0,  but  will  appear  to  see  the  image  at  0'  '.  The 
image  at  0'  is  of  course  virtual,  since  the  light  does  not  actu- 
ally focus  at  that  point.  If  the  eye  be  removed  no  image  will 
exist. 

485.  Spherical  Mirrors.  A  spherical  mirror  is  formed  from 
a  portion  of  a  spherical  shell,  a  section  of  a  spherical  mirror 
being  shown  in  Fig.  438.  The  opening  MM'  is  called  the  aper- 


LIGHT  321 

ture  of  the  mirror.  A  point  midway  between  M  and  M'  is 
the  vertex  V.  The  center  of  curvature  of  the  mirror  C  is  the 
center  of  the  sphere  of  which  the  mirror  is  a  part.  A  principal 
axis  is  a  straight  line  passing  through  the  center  of  curvature 
and  through  the  vertex.  A  secondary  axis  is  any  other  straight 
line  passing  through  the  center  of  curvature  and  cutting  the 
mirror  at  any  point  other  than  at  V.  The  line  CV  is  a  prin- 
cipal axis;  the  line  CS  is  a  secondary  axis.  When  we  consider 
a  spherical  mirror  from  the  concave  side  A,  it  is  called  a  con- 
cave mirror;  when  we  look  at  it  from  the  convex  side  B  it  is 
called  convex  mirror. 

486.   The  Principal  Focus  in  Spherical  Mirrors.     The  princi- 
pal focus  of  spherical  mirrors  is  the  point  at  which  rays  parallel 


FIG.  439  ^    FIG.  440 

to  the  principal  axis  come  to  a  focus,  Fig.  439.  For  concave 
mirrors  this  focus  is  real  and  a  point,  as  may  be  shown  by  allow- 
ing the  sun's  rays,  which  are  nearly  parallel,  to  fall  upon  the 
mirror. 

The  principal  focus  of  a  convex  mirror  is  a  virtual  focus 
and  is  the  point  at  which  rays  parallel  to  the  principal  axis 
appear  to  come  to  a  focus,  Fig.  440. 

487.  Relation  of  Image  and  Object  in  Spherical  Mirrors. 
Experiment,  (a)  If  a  candle  be  placed  on  the  principal  axis 
and  between  the  center  of  curvature  and  the  principal  focus 
of  a  spherical  mirror,  a  real  image  will  appear  upon  the  screen 
Fig.  441.  The  image  is  inverted,  real,  and  larger  than  the 
object,  (b)  If  now  the  candle  be  placed  in  the  position  of  the 


322 


HIGH   SCHOOL  PHYSICS 


screen  and  a  small  screen  be  placed  in  the  original  position  of 
the  candle,  a  small  but  very  bright  image  will  appear.     In  this 


FIG.  441 

case  the  image  is  again  real,  inverted,  but  smaller  than  the 
object,     (c)  If  now  the  mirror  be  brought  near  to  the  observer, 

so  that  the  candle  lies  between 
the  vertex  of  the  mirror  and  the 
principal  focus,  an  image  will  be 
seen  which  is  virtual,  erect,  and 
larger  than  thk  object,  Fig.  442. 

It  thus  appears  that  for  some 
cases  the  relation  of  the  image  to 
the  object  may  be  determined  ex- 
perimentally. It  is  sometimes  of 
importance,  also,  to  determine  this 
relation  graphically.  Suppose 
that  we  wish  to  determine  graph- 
ically the  position  and  character 
of  the  image  when  the  object  is 
placed  between  the  center  of  cur- 
vature and  the  principal  focus,  as 
in  Experiment  (a).  Let  the  arrow  AB,  Fig.  443,  represent 
the  object.  First,  from  the  point  A  draw  a  line  AD  parallel 


FIG.  442 


LIGHT 


323 


E 


FIG.  443 


to  the  principal  axis.     This  line  will  be  reflected  through  the 

principal  focus  in  the  direction  of  Da.      From    the  point   A 

draw  a  second  line  AC  through 

the   center  of  curvature   to  the 

mirror.     Since  this  line  is   nor- 

mal to  the  mirror,  it  will  be  re- 

flected   back    upon    itself,    thus 

forming  at  a  a  focus  which  will 

represent  the  point  of  the  image 

corresponding  to  A.     Now  draw 

two  similar  lines  from  the  point 

B.     These  lines  will  come  to  a 

focus  at  the  point  6,  forming  the  base  of  the  image.     Thus 

we  have  an  image  ab,  which  is  real,  inverted,  and  larger  than 

the  object. 

The  reason  for  drawing  at  least  two  rays  from  each  point 

in  the  object,  as  from  A,  is  because  at  least  two  rays  are  always 

required  to  determine  a  focus.     Of  course  as  many  other  rays 

may  be  drawn  to  the  mirror  as  desired;  these,  however,  would 

all  come  to  a  focus  at  the  point  a,  but  would  only  serve  to 

confuse  the  figure. 

In  determining  the  relation  of  the  object  to  the  image  in 

spherical  mirrors,  there  are  seven  important  cases,  which  should 

be  drawn  and  explained  as  outlined  in  the  following  topic. 
488.  Object  and  Image  in  Spherical  Mirrors.  1.  Given  an 
object  at  an  infinite  distance  from  a 
concave  mirror  to  find  the  position 
and  character  of  the  image.  Since 
the  rays  of  light  from  the  object  are 
parallel  to  the  principal  axis,  the 
image  formed  in  this  case  will  be 
real  and  a  point  at  the  principal 
focus,  Fig.  444. 
2.  Given  an  object  at  a  finite  distance  beyond  the  center  of 

curvature  to  find  the  position  and  character  of  the  image. 


/ 

\ 


V- 

v 


j,      444 


324 


HIGH   SCHOOL   PHYSICS 


The  image  is  real,  inverted,  smaller  than  the  object,  and  lies  be- 
tween the  principal  focus  and  the  center  of  curvature,  Fig.  445. 


FIG.  445 


FIG.  446 


3.  Object  at  the  center  of  curvature.     Since  in  this  case  we 
cannot  draw  a  ray  through  the  center  of  curvature  we  may 
determine  the  position  and  character  of  the  image  by  draw- 
ing, first,  from  the  object  to  the  mirror,  rays  parallel  to  the 
principal  axis  and  thence  back  through  the  principal  focus, 
and  second,  drawing  rays  from  the  object  to  the  mirror  through 
the  principal  focus  and  thence  back  parallel  to  the  principal 
axis.     It  thus  appears  that  the  image  is  real,  inverted,  and 
lies  upon  the  object  at  the  center  of  curvature,  Fig.  446. 

4.  Object  between  center  of  curvature  and  principal  focus. 
It  will  be  observed  that  this  is  the  reciprocal  of  case  2.      The 


FIG.  447 


image  is  real,  inverted,  larger  than  the  object,  and  lies  beyond 
the  center  of  curvature,  Fig.  447. 

5.   Object  at  the  principal  focus.     This  is  the  reverse  of 
case  1.     Since  the  rays  reflected  from  the  mirror  are  parallel, 


LIGHT 


325 


the  image  would  theoretically  be  at  an  infinite  distance  away. 
This  means  of  course  that  no  image  will  be  formed,  Fig.  448. 

6.  Object     between    the 
principal  focus  and  the  mir- 
ror.     The     rays     reflected 
from  the  mirror  are  diver- 
gent and  hence  will  never 
come  to  a  focus,  and  no  real 
image   will    therefore    be 

formed.     In  case  an  eye  be  FIG.  448 

stationed    in    front   of    the 

mirror  a  virtual  image  will  be  formed  back  of  the  mirror. 
That  is,  in  this  case  the  image  is  virtual,  erect,  larger  than 

the  object,  and  ap- 
pears to  lie  back  of 
the  mirror,  Fig.  449. 
If  a  spherical  mir- 
ror be  brought  near 
to  the  face  so  that 
the  eye  lies  between 
the  principal  focus 
and  the  mirror  a  vir- 
tual and  magnified  image  of  the  face  may  be  obtained,  as 
illustrated  in  Fig.  450. 

7.  Object  in  front  of  convex  mirror.     In  this  case  also  the 


FIG.  449 


FIG.  450 


326 


HIGH   SCHOOL  PHYSICS 


image  is  virtual,  smaller  than  the  object,  and  appears  to  lie 
between  the  mirror  and  the  principal  focus,  Fig.  451. 

If  one  look  into  a  convex  mirror  a  minified  and  virtual  image 
may  be  seen,  as  shown  in  Fig.  452. 

Formulae  for  Images  Formed  by  Mirrors,  Supplement,  587. 


FIG.  452 

489.  Spherical  Aberration.  In  the  preceding  cases  of  the 
spherical  mirror,  it  has  been  taken  for  granted  that  all  rays 
parallel  to  the  principal  axis  after  being  reflected  pass  through 
the  principal  focus.  This,  however,  is  not  true  for  those  rays 
which  fall  upon  the  mirror  near  the  extremities  M  and  M'. 
The  reflected  rays  for  this  portion  of  the  mirror  shown  in  Fig. 
453  do  not  pass  through  the  principal  focus.  This  failure  of 
part  of  the  light  to  pass  through  the  principal  focus  is  called 
spherical  aberration. 


FIG.  453 


FIG.  454.  —  Caustic 


LIGHT  327 

Spherical  aberration  in  the  case  of  a  spherical  reflecting  sur- 
face gives  rise  to  a  curved  line  of  light  called  the  caustic.  A 
caustic  curve  can  be  demonstrated  experimentally  by  allowing 
rays  of  light  to  fall  upon  the  concave  surface  of  a  strip  of  pol- 
ished metal  (bright  tin)  bent  into  the  form  of  a  circular  arc, 
Fig.  454,  the  reflected  light  being  received  on  a  piece  of  white 
paper  upon  which  the  strip  of  metal  rests.  This  same  effect 
may  be  seen  by  allowing  the  sunlight  to  fall  upon  the  inside  of 
a  gold  finger  ring  placed  upon  a  piece  of  white  paper. 

490.  Diffused  Light.  If  a  beam  of  light  fall  upon  a  smooth 
surface  it  will  be  regularly  reflected,  as  shown  in  Fig.  455.  If 
this  light  be  received  by  the  eye,  the  latter  will  see  not  the 
reflecting  surface,  but  the  source  of  light.  For  example,  light 
reflected  from  the  surface  of  highly  polished  furniture,  or  the 
surface  of  still  water,  shows  this  property. 


FIG.  455  FIG.  456 

If,  on  the  other  hand,  a  beam  of  light  fall  upon  a  body  hav- 
ing an  irregular  surface,  such  as  a  piece  of  white  paper  or  the 
wall  of  a  room,  the  light  is  scattered  in  all  directions,  Fig.  456. 
This  is  called  diffused  light.  It  must  not  be  imagined,  however, 
that  diffused  light  does  not  obey  the  laws  of  reflection,  for  it 
does,  the  angle  of  reflection  for  each  ray  in  every  case  being 
equal  to  the  angle  of  incidence.  The  scattering  of  the  rays 
is  due  to  the  irregularities  in  the  reflecting  surface.  It  is  by 
means  of  this  diffused  light  that  we  are  enabled  to  see  clearly 
the  outline  of  bodies.  If  every  object  possessed  a  polished 
surface  we  would  see  only  the  light  of  the  source  and  would 
not  be  able  to  make  out  clearly  and  definitely  the  outline  and 
nature  of  the  reflecting  surface. 


328 


HIGH  SCHOOL  PHYSICS 


REFRACTION 

491.  Refraction.  Experiment.  If  a  beam  of  light  be 
allowed  to  fall  upon  the  surface  of  water  at  0,  Fig.  457,  part  of 
it  will  be  reflected  to  E,  according  to  the  laws  of  reflection, 
and  a  part  will  be  refracted  to  B.  Refraction  is  the  bending  of 
a  ray  of  light  due  to  passing  from  a  medium  of  one  density  to 
that  of  another  density.  The  angle  i  is  the  angle  of  incidence, 
the  angle  COB  is  the  angle  of  refraction,  and  BOD  the  angle 
of  deviation. 


A 


FIG.  457 


FIG.  458 


492.  Explanation  of  Refraction.     Imagine  a  series  of  wave 
fronts  advancing  in  the  direction  AO,  Fig.  458.     When  the 
portion  of  the  wave  marked  6  strikes  the  surface  of  the  water 
its  speed  is  retarded;   a,  therefore,  moves  faster  than  6,  hence 
the  wave  front  is  bent  downward,  as  shown,  and  the  direction 
of  the  motion  is  changed  from  AO  to  OB.     After  a  wave  once 
passes  into  a  medium  both  portions  of  the  wave  front,  a  and  6, 
move  forward  with  the  same  speed;  therefore  the  line  of  direc- 
tion OB  is  a  straight  line.     Refraction  of  light  is  due  to  a 
change  in  velocity  of  one  portion  of  a  wave  front  as  compared 
with  that  of  another,  as  the  wave  passes  from  one  medium  to 
another  of  different  density. 

493.  Illustrations  of  Refraction.     Experiment.     If  a  coin  be 


LIGHT 


329 


placed  in  the  bottom  of  a  cup  so  that  it  lies  just  beyond 
the  range  of  vision,  Fig.  459,  and  the  cup  then  be  filled  with 
water,  the  coin  will  gradually  come  into  view.     This  is  due  to 
the  fact  that  the  ray  of  light  from  the 
coin  to  the  eye  is  bent  away  from  the 
normal  at  the  surface.     The  eye  in  look- 
ing along  the  line  appears  to  see  the 
coin  as  if  elevated. 

If  the  stick  be  thrust  into  water  in 
the  direction  A,  Fig.  460,  it  will  ap- 
pear to  be  bent  away  from  the  ob- 
server; if  it  be  thrust  in  the  direction 
B  it  will  appear  to  be  bent  toward 
the  observer.  The  refraction  of  light  thus  not  only  accounts 
for  the  apparent  bending  of  the  stick,  but  also  for  the  fact  that 
the  bottom  of  a  vessel  containing  water,  or  the  bottom  of  a 
pond,  appears  to  be  nearer  the  surface  than  it  really  is.  Both 


FIG.  459 


FIG.  460 

the  apparent  displacement  of  an  object  and  the  shoaling  of 
water  are  well  illustrated  by  Fig.  461.  To  the  boy  on  the  bank 
the  fish  which  is  at  b  appears  to  be  at  a.  To  the  man  on  the 
bridge  the  distance  from  the  surface  of  the  water  to  the  fish 
appears  to  be  less  than  it  really  is.  When  looking  vertically 
downward  at  the  bottom  of  a  vessel  filled  with  water  the  appar- 
ent distance  from  the  surface  to  the  bottom  is  three-fourths 
of  the  true  distance.  This  may  be  shown  by  looking  at  the 


330 


HIGH  SCHOOL  PHYSICS 


bottom  of  a  tall  glass  vessel  filled  with  water.     If  the  finger  be 
placed  on  the  side  of  the  vessel  at  the  point  where  the  bottom 


FIG.  461 


FIG.  462 


appears  to  be,  it  will  be  found  that  the  point  touched  by  the 
finger  will  be  about  three-fourths  the  entire  depth  of  the  water. 


FIG.  463.  — Mirage 

494.  Refraction  in  Air.  An  interesting  illustration  of  refrac- 
tion occurs  in  the  bending  of  the  rays  of  light  in  passing  through 
portions  of  the  atmosphere  having  different  densities.  A  ray 


LIGHT 


331 


of  light,  for  example,  from  the  star  S  will  be  refracted  in  pass- 
ing from  one  layer  of  air  to  another,  as  shown  in  Fig.  462.  An 
observer  on  the  earth  at  0  will  appear  to  see  the  star  in  the 
position  S'.  The  apparent  position  of  the  body  is  higher 
than  its  real  position.  It  thus  frequently  happens  that  the 
sun  is  visible  while  yet  actually  belbw  the  horizon. 

The  mirage  is  a  phenomenon  frequently  observed  in  deserts, 
in  which  the  traveler  sees  the  image  of  distant  objects,  such  as 
palm  trees,  etc.,  usually  by  refraction.  The  explanation  of  the 
mirage  lies  mainly  in  the  fact  of  the  refraction  of  light  through 
layers  of  air  of  different  density.  A  phenomenon  somewhat 
similar  to  the  mirage  of  the  desert  is  occasionally  seen  at  sea 
in  still,  hot  weather,  in  which  the  image  of  a  distant  ship 
appears  in  the  sky,  sometimes  upright,  sometimes  inverted, 
as  shown  in  Fig.  463. 


FIG.  464 


FIG.  465 


495.  The  Law  of  Refraction.     When  a  ray  of  light  passes  from 
a  rare  to  a  dense  medium,  as  from  air  to  water  or  glass,  it  is  bent 
toward  the  normal,  Fig.  464;   when  it  passes  from  a  dense  to  a 
rare  medium  it  is  bent  away  from  the  normal,  Fig.  465. 

496.  Refraction  of  a  Ray  through  a  Parallel  Plate.     Let  a 
ray  of  light  AB,  Fig.  466,  be  incident   upon  the  surface  of  a 
piece  of  plate  glass  at  the  point  B.     Let  BD  represent  the 
refracted  ray.     At  B  the  ray  is  bent  toward  the  normal  as  it> 
passes  into  the  denser  medium,  and  at  C  it  is  bent  away  from 


332 


HIGH  SCHOOL  PHYSICS 


the  normal  as  it  passes  out.  The  refraction  at  C  is  equal  to 
that  at  B  and  in  the  opposite  direction.  The  ray  CD  is  there- 
fore parallel  to  AB.  When  a  ray  passes  through  a  parallel  plate 
its  direction  is  unchanged;  it  suffers  only  lateral  displacement. 

497.  Refraction  of  a  Ray  through  a  Prism.  Experiment. 
Let  a  ray  of  light  fall  upon  a  prism  as  shown  in  Fig.  467. 
On  entering  the  prism  it  is  bent  toward  the  normal  and  on 
emerging  it  is  bent  away  from  the  normal.  An  eye  will, 
therefore,  appear  to  see  the  object  as  if  elevated  in  line  with 
the  refracted  ray. 


FIG.  466 


FIG.  467 


498.  Index  of  Refraction.     We  have  learned  in  a  preceding 
topic  (Art.  476)  that  the  velocity  of  light  in  a  vacuum  is  greater 
than  in  air,  and  the  velocity  in  air  is  greater  than  in  water,  etc. 
Now  it  is  possible  to  measure  the  relative  velocities  of  light  in 
any  two  media  with  great  accuracy.     For  example,  the  velocity 
of  light  in  a  vacuum  is  to  the  velocity  of  light  in  water  as  4 :  3 ; 
that  is,  the  velocity  of  light  in  air  is  1.333  times  as  great  as  in 
water. 

The  index  of  refraction  of  any  substance  may  be  defined,  then, 
as  the  ratio  of  the  velocity  of  light  in  a  vacuum  to  the  velocity 
of  light  in  that  substance.  (Supplement,  589.)  The  index  of 
refraction  of  water  is  1.33;  crown  glass  1.53;  flint  glass  1.61; 
diamond  2.47. 

499.  Critical  Angle.     Consider  a  source  of  light  at  A  in  the 
medium  water,  Fig.  468.     A  ray  from  A  to  B  will  be  reflected 
away  from  the  normal  to  C.     For  this  ray  the  angle  of  inci- 


LIGHT 


333 


dence  is  ABN'  and  the  angle  of  refraction  CBN.  A  ray  of 
light  from  E  to  £  will  be  refracted  along  the  surface  of  the 
water  to  D.  In  this  case  the  angle  of  incidence  is  EBN'  and 


A    N 
FIG.  468 


the  angle  of  refraction  DB  N  is  90°.  The  angle  EB  N'  is  called 
the  critical  angle.  When  we  speak  of  the  critical  angle  we  always 
consider  the  light  as  passing  from  the  dense  to  the  rare  medium, 
as  from  water  to  air.  The  critical  angle 
is  an  angle  of  incidence  such  that  the 
angle  of  refraction  is  90°. 

Now  if  we  consider  the  ray  of  light  as 
coming  from  a  source  F,  the  ray  will  not 
emerge  from  the  surface  at  all,  but  will 
be  totally  reflected  at  the  point  B  in 
the  direction  BG.  A  person  standing  at 
F  and  looking  at  the  surface  of  the 
water  at  B  will  see  the  bottom  at  G\ 
that  is  to  say,  the  surface  of  the  water 
will  act  like  a  plane  mirror. 

500.  Total  Internal  Reflection.  When 
the  angle  of  incidence  of  a  ray  of  light 
passing  from  a  dense  to  a  rare  medium 
is  greater  than  the  critical  angle,  we 
have  total  internal  reflection.  If  a  spoon  be  placed  in  a  tum- 
bler of  water  and  the  surface  of  the  water  be  viewed  from 


FIG.  469 


334  HIGH  SCHOOL  PHYSICS 

below  at  an  angle  greater  than  the  critical  angle,  the  spoon 
may  be  seen  by  reflection  from  the  surface,  Fig.  469.  The 
critical  angle  for  water  is  48°  30';  for  flint  glass  38°  41';  for 
diamond  23°  41 ' .  Substances  which  have  a  high  index  of 
refraction,  as  for  example  the  diamond,  have  a  relatively 
small  critical  angle,  and  therefore,  most  of  the  light  falling 
upon  the  surface  from  the  interior  suffers  total  internal  reflec- 
tion. The  large  proportion  of  light  which  is  totally  reflected 
in  the  diamond  gives  rise  to  the  great  brilliancy  of  this 
gem. 

A  beautiful  illustration  of  total  reflection  is  furnished  by  a 
stream  of  water  flowing  from  a  tank,  Fig.  470,  having  in  the 

side  opposite  the  orifice  a  lens  by 
means  of  which  a  strong  beam  of 
light  from  the  sun  or  an  electric 
arc  may  be  concentrated  within 
the  jet.  The  light  strikes  the  in- 
terior surface  of  the  stream  of 
water  at  an  angle  greater  than 
the  critical  angle  and  thus  suffers 
total  internal  reflection.  The  light 
is  held  within  the  stream  until, 
FIG.  470  after  repeated  reflection,  it  strikes 

the    bottom    of    the    receptacle, 

where  it  shows  as  a  bright  spot.  A  goblet  held  in  the  stream 
is  filled  with  bright  light,  which  gives  rise  to  the  name  "  foun- 
tain of  fire."  The  brilliant  display  seen  in  electrical  fountains 
depends  upon  this  principle. 

LENSES 

501.  The  Lens.  A  lens  is  a  transparent  medium  having  two 
curved  surfaces  or  one  curved  and  one  plane  surface.  There  are 
two  general  classes  of  lenses,  convex  and  concave. 

A  convex  lens  is  one  that  is  thicker  at  the  middle  than  at  the 
edges.  Convex  lenses  are  divided  into  three  sub-classes,  as 


LIGHT 


335 


FIG.  471 

Convex  Lenses 


FIG.  472 
Concave  Lenses 


shown  in  Fig.  471;  namely,  double-convex,  plano-convex,  and 
concave-convex. 

A  concave  lens  is  one  that  is  thinner  at  the  middle  than  at  the 
edges.  Concave  lenses  are  also  divided  into  three  sub-classes, 
Fig.  472,  double-concave, 
plano-concave,  and  convex- 
concave. 

502.  Terms  Used  in  Con- 
nection with  Lenses.   Since 
a  lens  is  made  up  of  the 
intersection  of  two  spheres, 

or  of  one  sphere  and  a  plane,  we  may  speak  of  the  center  of 
curvature  of  the  lens  as  the  center  of  the  sphere  of  which  its 
face  is  a  part.  Since  a  lens  always  has  two  faces,  it  therefore 

always  has   two   centers  of  curva- 
"X     ,''  ture.     A  straight  line  PP',  drawn 

through  the  centers  of  curvature  of 
a  lens,  is  called  the  principal  axis, 
Fig.  473.  The  optical  center  of  the 
lens  0  is  a  point  through  which  a 
ray  may  pass  without  having  its  di- 
rection changed.  In  double-convex 
and  double-concave  lenses,  having 
surfaces  of  equal  curvatures,  the 
optical  center  is  at  the  center  of 
the  lens.  In  some  cases,  however,  the  optical  center  may  lie 
entirely  outside  the  lens.  In  this  text  we  shall  consider  in 
every  case  lenses  having  optical  centers  at  their  geometric 
centers. 

The  principal  focus  of  a  lens  is  the  point  on  the  principal  axis 
at  which  rays  parallel  to  the  principal  axis  come  to  a  focus. 
The  distance  from  the  principal  focus  to  the  optical  center  is 
the  focal  length  of  the  lens. 

503.  The  Relation  of  the  Thickness  of  a  Lens  to  its  Focal 
Length.     The  effect  of  the  curvature  of  a  lens  upon  parallel 


— P 


-P— 


FIG.  473 


336 


HIGH  SCHOOL  PHYSICS 


rays  of  light  is  illustrated  in  Fig.  474.  The  lens  having  the 
greater  curvature,  that  is,  the  thick  lens,  has  the  shorter  focal 
length.  This  effect  of  the  curvature  of  the  lens  upon  its  focal 
length  may  be  expressed  by  the  statement,  the  thicker  the  lens 
the  shorter  its  focal  length. 

504.  The  Effect  of  Lenses  on  Parallel  Rays.  Since  rays  of 
light  falling  upon  a  lens  are  bent  toward  the  normal  on  entering 
the  lens  and  away  from  the  normal  on  leaving  it,  the  general 
effect  of  lenses  may  be  stated  as  follows :  (a)  Convex  lenses  are 
convergent;  they  cause  the  rays  of  light  to  come  to  a  focus, 
Fig.  475.  (b)  Concave  lenses  are  divergent,  Fig.  476. 


V 
FIG.  475 


FIG.  474 


FIG.  476 


505.  Spherical  Aberration  in  Lenses.  In  the  preceding 
topics  it  has  been  assumed  for  the  sake  of  simplicity  that  all 
rays  which  pass  through  the  lens  also  pass  through  the  prin- 
cipal focus.  This,  however,  is 
not  the  case.  In  thick  convex 
lenses  those  rays  which  pass 
through  near  the  edge  of  the 
lens  cross  the  principal  axis 
nearer  the  lens  than  do  those 
rays  which  pass  through  near 
the  principal  axis,  Fig.  477. 
This  failure  of  all  the  rays  to 

pass  through  a  common  point  produces  a  blurring  of  the  im- 
age.    Spherical  aberration  is  the  blurring  of  the  image  due  to 


FIG.  477 


LIGHT  337 

the  failure  of  the  marginal  rays  to  pass  through  the  principal 
focus. 

Spherical  aberration  in  a  lens  may  be  remedied  by  cutting 
off  the  marginal  rays  by  means  of  a  screen  or  diaphragm.  The 
use  of  a  diaphragm  makes  the  image  sharper  in  outline,  but 
less  bright.  In  large  lenses,  such  as  are  used  in  telescopes, 
spherical  aberration  is  diminished  by  making  the  curvature  of 
the  lens  less  toward  the  edge,  thus  tending  to  bring  all  parallel 
rays  to  the  same  focus. 


FIG.  478 

506.  Illustration  of  Images  Formed  by  Lenses.  Experi- 
ment, (a)  Place  a  candle  some  distance  from  a  screen  in  a 
darkened  room.  Next  place  a  convex  lens  between  the  candle 
and  the  screen,  and  relatively  near  the  candle.  Adjust  the 
position  of  the  lens  until  a  clear  image  of  the  candle  is  thrown 
upon  the  screen,  Fig.  478.  The  image  is  real,  inverted,  and 
larger  than  the  candle.  Experiment,  (b)  Now  change  the 
position  of  the  lens,  keeping  it  between  the  candle  and  the 
screen,  but  relatively  near  the  screen.  A  second  position  will 
be  found  at  which  an  image  again  appears  upon  the  screen. 
In  this  case  the  image  is  real,  inverted,  and  much  smaller  than 
the  object. 


338 


HIGH   SCHOOL  PHYSICS 


Thus,  as  in  the  Case  of  the  mirror,  the  size  of  the  image  formed 
by  a  lens  depends  upon  its  position  with  respect  to  the  object 
and  the  screen. 

507.  To  Find  by  Drawing  the  Position  and  Character  of  the 
Image.  Suppose  that  the  object  be  placed  beyond  the  prin- 
cipal focus  F,  as  exemplified  by  Experiment  (a)  of  the  preceding 
topic.  Fig.  479  illustrates  the  relative  position  of  the  lens  with 


FIG.  479 

respect  to  the  object  AB.  Now  in  order  to  determine  the  posi- 
tion and  character  of  the  image,  it  is  necessary  to  draw  at  least 
two  rays  from  each  of  the  points  A  and  B  of  the  object  to  the 
lens.  We  select  two  rays  the  direction  of  which  can  readily  be 
determined;  these  are  respectively  a  ray  parallel  to  the  principal 
axis,  which  after  reflection  passes  through  the  principal  focus  F 
in  the  direction  Fb,  and  the  ray  A  b  passing  through  the  opti- 
cal center.  In  a  like  manner  we  draw  from  the  point  B  two 
similar  rays,  one  passing  through  the  principal  focus  and  the 
other  passing  through  the  optical  center.  Thus  we  have 
formed  at  ab  a  graphic  representation  of  the  image.  It  is 
real,  inverted,  and  larger  than  the  object. 

508.  Relation  of  Image  to  Object.  There  are  seven  general 
cases  illustrating  the  relation  of  the  image  formed  by  the  lens 
to  the  object.  These  cases  may  be  demonstrated  graphically 
as  follows: 

1.   Given  an  object  at  a  great  distance  from  the  lens  such 


LIGHT 


339 


that  the  rays  from  the  object  to  the  lens  are  parallel  to  the 
principal  axis,  to  find  the  position  and  character  of  the  image. 
The  image  is  real,  a  point,  and  lies  at  the  principal  focus, 
Fig.  480. 

A 


FIG.  480 


2.  Given  an  object  at  a  finite  distance  from  a  lens  greater 
than  twice  the  focal  distance  to  find  the  position  and  character 
of  the  image.  The  image  is  real,  inverted,  smaller  than  the 
object,  and  lies  beyond  the  principal  focus,  Fig.  481. 


FIG.  481 


3.  Object  at  twice  the  focal  distance  from  the  lens.  The 
image  is  real,  inverted,  the  same  size  as  the  object,  and  as 
far  back  of  the  lens  as  the  object  is  in  front  of  it,  Fig.  482. 


FIG.  482 


4.  Object  at  a  point  less  than  twice  the  focal  distance,  but 
greater  than  the  focal  distance.  The  image  is  real,  inverted, 
and  larger  than  the  object,  Fig.  483. 


340 


HIGH  SCHOOL  PHYSICS 


5.   Object  at  the  principal  focus.     Since  the  rays  are  parallel 

'b 


FIG.  483 

to  the  principal  axis,  the  image  is  formed  theoretically  at  an 
infinite  distance  from  the  lens,  Fig.  484.  This  is  the  converse 
of  case  1. 


FIG.  484 

6.  Object  between  the  lens  and  the  principal  focus.  The 
rays  on  leaving  the  lens  are  divergent,  hence  no  real  image  is 
formed.  If  an  eye  be  placed  in  a  position  to  receive  these  diver- 
gent rays,  an  image  will  appear  to  be  at  ab.  This  image  is 
virtual,  erect,  and  larger  than  the  object,  Fig.  485.  This  is 
the  case  of  the  simple  microscope. 


FIG.  485 


LIGHT 


341 


7.  To  find  the  position  and  character  of  the  image  formed 
by  a  convex  lens.  Let  AB  represent  the  object.  The  trans- 
mitted rays  are  divergent,  hence  no  real  image  will  be  formed. 


A 


/O   I 


FIG.  486 


A  virtual  image  will  appear  at  ab.     The   image   is  virtual, 
erect,  and  smaller  than  the  object,  Fig.  486. 

Formulae  for  Images  Formed  by  Lenses,  see  Supplement,  588. 


OPTICAL  INSTRUMENTS 

509.   The    Simple    Microscope.     The   simple  microscope  or 
common  magnifier,  such  as  is  used  in  examining  botanical  and 


FIG.  487 


FIG.  488 
Magnification  by  Simple  Microscope 


zoological  specimens  and  similar  objects,  Fig.  487,  illustrates 
that  case  of  the  convex  lens  in  which  the  object  is  placed 
between  the  lens  and  the  principal  focus  (case  6).  It  gives  a 
virtual  and  magnified  image  of  the  object,  Fig.  488. 


342  HIGH  SCHOOL  PHYSICS 

510.  The  Eye.  We  have  in  the  case  of  the  human  eye  a 
very  remarkable  application  of  the  principle  of  the  formation 
of  real  images  by  a  convex  lens.  The  characteristic  parts  of  the 
eye  are  shown  in  Fig.  489.  The  outer  portion  of  the  eyeball 


FIG.  489 

s,  consists  of  a  tough  covering  called  the  sclerotic  coat;  b  is 
the  choroid  coat,  containing  a  black  pigment,  the  function  of 
which  is  to  prevent  internal  reflection  of  the  light;  r  is  the 
retina,  formed  by  an  expansion  of  the  optic  nerve;  covering 
the  front  of  the  eye  is  the  cornea  c,  a  transparent  medium ;  i 
is  the  iris,  which  gives  the  eye  its  characteristic  color  and  the 
function  of  which  is  to  regulate  the  quantity  of  light  entering 
through  the  pupil  p.  The  three  refracting  media  are  aq,  the 
aqueous  humor;  cl,  the  crystalline  lens;  and  v,  the  vitreous 
humor.  The  most  important  of  the  three,  from  an  optical 
viewpoint,  is  the  crystalline  lens. 

511.  The  Image  upon  the  Retina.  The  image  formed  upon 
the  retina  by  an  object  situated  in  front  of  the  eye  is  real,  smaller 
than  the  object,  and  inverted.  If  a  candle  be  held  in  front  of 
an  eye  taken  from  a  freshly  killed  animal,  it  is  possible  under 
satisfactory  conditions  to  see  the  inverted  image  formed  upon 
the  retina,  as  shown  in  Fig.  490.  The  question  naturally  arises 
as  to  why  it  is  that  we  can  see  objects  erect  when  the  image 
upon  the  retina  is  inverted.  The  explanation  probably  lies  in 
the  fact  that  our  judgments  of  the  true  position  of  bodies 


LIGHT 


343 


with  respect  to  each  other  is  based  primarily  upon  experiences 
other  than  those  of  sight.  It  is  said  that  the  blind  upon  recov- 
ering sight  often  find  it  necessary  at  first  to  use  the  sense  of 
touch  in  determining  the  true  position  of  bodies. 


FIG.  490 

In  using  the  camera  it  is  necessary  to  focus  the  instrument 
by  moving  either  the  screen  or  the  lens  back  and  forth  so  as 
to  bring  the  image  upon  the  plate.  In  the  case  of  the  eye, 
however,  this  focusing  is  accomplished  automatically  by  chang- 
ing the  convexity  of  the  crystalline  lens.  It  is  very  remark- 
able that  we  can  involuntarily  and  almost  instantly  change 
the  shape  of  the  crystalline  lens  so  that  the  image  of  an  object 
only  a  few  inches  distant,  or  an  object  miles  away,  may  be  dis- 
tinctly focused  upon  the  retina. 

512.  The  Abnormal  Eye.  The  three  most  common  defects 
of  the  eye  are :  (a)  nearsightedness,  (b)  farsightedness,  (c)  astig- 
matism. 


FIG.  491 


FIG.  492 


FIG.  493 


In  the  normal  eye  light  from  a  given  object  is  focused  exactly 
upon  the  retina,  Fig.  491.  The  nearsighted  eye  is  one  in  which 
the  distance  from  the  lens  to  the  retina  is  so  great  that  the 
image  cannot  be  properly  focused  upon  the  retina,  Fig.  492. 
Persons  having  such  eyes  are  said  to  be  nearsighted,  because 


344 


HIGH  SCHOOL  PHYSICS 


they  have  to  bring  the  object  very  near  the  eye  in  order  to  see 
it  distinctly.  Nearsightedness  is  remedied  by  the  use  of  con- 
cave glasses,  which  diverge  the  rays  and  thus  throw  the  image 
farther  back  upon  the  retina,  Fig.  493. 


FIG.  494 


FIG.  495 


The  farsighted  eye  is  one  in  which  the  image  tends  to  form 
beyond  the  retina,  Fig.  494.  The  remedy  for  farsightedness 
lies  in  the  use  of  convex  glasses,  Fig.  495. 

613.  Astigmatism.  Astigmatism  is  a  defect  of  the  eye  due  to 
a  distortion  of  the  image  on  the  retina,  which  may  be  caused 

either  by  irregularities  in  the  shape 
of  the  eyeball  or  a  lack  of  sym- 
metry in  the  crystalline  lens.  The 
defect  of  astigmatism  may  be  de- 
tected by  looking  at  a  series  of 
radiating  lines,  Fig.  496.  If  the 
eye  be  astigmatic  the  radiating 
lines  will  not  be  seen  with  equal 
distinctness.  Astigmatism  may  be 
corrected  by  the  use  of  specially 
ground  lenses  which  compensate  for 
the  defects  of  curvature  in  the  eye. 
514.  The  Visual  Angle  and  Apparent  Size  of  Objects.  The 
visual  angle  is  the  angle  formed  by  rays  passing  from  the  extrem- 
ities of  an  object  and  intersecting  at  the  eye,  Fig.  497.  The 
size  of  this  angle  depends  (a)  upon  the  size  of  the  object  and 
(b)  upon  its  distance  from  the  eye;  the  greater  the  distance  the 
less  the  visual  angle.  Now  the  apparent  size  of  an  object 
depends  upon  the  size  of  the  visual  angle,  because  this  angle 


FIG  496 


LIGHT 


345 


determines  the  size  of  the  image  formed  upon  the  retina. 
Therefore  the  smaller  the  visual  angle  the  smaller  will  be  the 
image  on  the  retina,  and  consequently,  the  smaller  the  appar- 
ent size  of  the  object.  If  one  look  along  a  railroad  track  the 


FIG.  497 

rails  appear  to  approach  each  other  and  the  ties  to  grow  shorter, 
due  to  the  fact  that  the  visual  angle  diminishes  as  the  distance 
increases.  We  are  enabled  to  judge  of  the  real  height  and  size 
of  objects  which  are  at  a  considerable  distance  only  by  calling 
on  our  past  experiences  and  judgments. 

515.  Distance  of  Distinct  Vision.  Distinctness  of  vision 
depends  upon  thejsize  of  the  image  formed  on  the  retina;  there- 
fore it  may  be  assumed  that  the  nearer  an  object  is  brought  to 
the  eye  the  more  distinct  it  will  become.  Common  experience 
teaches  us  that  this  is  true  only  within  certain  limits,  which 
may  be  determined  by  experiment.  If  the  page  of  a  book  be 
held  off  at  arm's  length  the  printed  matter  will  not  be  distinct 
enough  for  most  people  to  read  with  ease.  Upon  bringing  the 
book  gradually  nearer,  however,  the  type  will  become  more 
distinct  as  the  page  approaches,  up  to  a  certain  point,  from 
which  position  it  will  gradually  grow  dim  again.  The  distance 
at  which  the  type  appears  most  distinct  is  called  the  distance 
of  distinct  vision;  it  is  for  most  normal  eyes  about  10  inches 
or  25  centimeters.  The  limit  of  distinct  vision  is  determined 
by  the  power  of  the  crystalline  lens  to  change  its  shape  and 
thus  focus  the  image  upon  the  retina. 

516.  The  Camera.  The  photographer's  camera  is  an  instru- 
ment used  for  the  printing  of  pictures  by  the  action  of  light 


346 


HIGH   SCHOOL  PHYSICS 


upon  chemically  prepared  films.  It  consists  of  a  light-proof 
box  having  an  adjustable  lens,  Fig.  498.  The  essential  fea- 
tures of  the  camera  consist  of  the  adjustment  of  the  lens  L, 


FIG.  498 


FIG.  499 


Fig.  499,  until  a  sharp  image  of  the  object  to  be  photographed 
is  formed  upon  the  film.  The  image  formed  in  the  camera  is 
real  and  inverted. 

Compound  Microscope,  Telescope,  and  other  Optical  Instru- 
ments, see  Supplement,  590  and  591. 

517.  Duration  of  Visual  Impressions.  The  duration  of  a 
visual  impression  depends  on  the  sensitiveness  of  the  retina  and 
the  intensity  of  the  light,  the  average  time  being  estimated  as 
about  half  a  second.  Distinct  impressions,  therefore,  cannot 
be  made  upon  the  retina  unless  they  succeed  each  other  at 
intervals  greater  than  that  of  the  duration  of  visual  impres- 
sions for  the  given  individual.  It  is  this  persistence  of  impres- 
sions on  the  retina  that  makes  a  swiftly  moving  object  appear 
as  a  continuous  line.  Thus  the  spokes  of  a  rapidly  revolving 
wheel  appear  to  blend  into  one  another,  and  in  a  similar  manner 
a  burning  stick  whirled  rapidly  around  at  night  gives  the 


LIGHT 


347 


impression  of  a  continuous  circle  of  flame.  For  this  reason, 
also,  shooting  stars  appear  to  have  luminous  tails  behind  them, 
and  an  electric  arc  lamp,  fed  with  an  alternating  current  of 
frequency  greater  than  25  cycles  per  second,  appears  to  give 
a  continuous  light.  If  the  arc  be  photographed,  however,  on 
a  rapidly  moving  plate,  it  will  be  found  that  the  light  is  extin- 
guished, that  is,  diminishes  to  zero  intensity,  with  every  reversal 
of  the  current,  thus  showing  that  it  is  really  discontinuous. 

518.  Visual  Judgments.  The  eye  has  been  likened  to  a 
camera,  and  so  far  as  the  physical  principles  involved  are  con- 
cerned, the  likeness  is  very 
striking.  The  impressions 
received  from  the  eye,  how- 
ever, are  quite  different  from 
those  given  by  a  photo- 
graph, and  for  two  reasons. 
In  the  first  place  a  photo- 
graph gives  a  picture  of  an 
object  in  a  given  position, 
while  the  brain  receives 
from  the  eye  a  composite  impression.  The  difference  between 
these  two  effects  is  very  well  shown  in  the  comparison  of  a 
\  A  /  snap-shot  photograph  of  a  horse  in 

the  act  of  running,  with  that  of  a 
\  simultaneous  impression  received 
from  the  eye,  Fig.  500.  And  in  the 
second  place,  our  judgments  of  the 
position,  size,  and  form  of  objects 
depend  not  only  upon  the '  images 
formed  by  the  eye,  but  also,  as  has  already  been  explained  in 
Art.  514,  upon  our  past  experience.  Sometimes  our  judgment 
is  at  fault,  however,  giving  rise  to  optical  illusions  of  various 
sorts.  Thus  in  Fig.  501  the  two  horizontal  lines  are  of  exactly 
the  same  length.  Line  A  appears  to  be  longer  than  B  because 
of  the  effect  of  the  oblique  lines  at  the  ends. 


FIG.  500 


FIG.  501 


348  HIGH  SCHOOL  PHYSICS 

COLOR  AND  DISPERSION 

519.  Color.  Color  is  a  sensation  which  depends  upon  the  nature 
of  the  light  falling  upon  the  retina.     The  color  which  a  given 
light  is  capable  of  producing  depends  upon  its  wave  length, 
red  being  due  to  the  longest  wave  length  and  violet  to  the 
shortest.      We  cannot  properly  speak  of  red  light  or  blue  light, 
since  the  waves  which  give  rise  to  those  colors  are  in  themselves 
colorless.     When  light  waves   making  395  trillion  vibrations 
per  second  fall  upon  the  retina  they  give  rise  to  a  sensa- 
tion which  we  have  been  taught  to  call  red;  and  likewise,  light 
waves  making  760  trillion  vibrations  per  second  give  rise  to  a 
sensation  which  we  call  violet.     In  a  similar  manner  we  can 
account  for  all  the  intermediate  color  sensations. 

It  must  be  noted  here  that  light  is  the  cause  of  color  and  that 
the  two  important  conditions  for  the  production  of  color  are 
(a)  the  presence  of  light  and  (b)  a  sensorium  (nerves  and  nerve 
centersJTolreceive  the  impression.  If  there  were,  therefore,  no 
eye  to  receive  the  impressions  of  the  light  waves,  there  would 
be  no  color. 

The  following  table  gives  a  list  of  the  colors  of  the  solar 
spectrum,  together  with  the  wave  lengths  and  vibration  rate 
of  each. 

Length  of  waves  No.  of  vibrations 

in  millimeters  per  second 

Red A  000760  395,000,000,000,000 

Orange.... C  000656  458,000,000,000,000 

Yellow D  000589  510,000,000,000,000 

Green E  000527  570,000,000,000,000 

Blue, F  000486  618,000,000,000,000 

Indigo  .  .  . .  G  .000431  697,000,000,000,000 

Violet H  000397  760,000,000,000,000 

520.  The  Spectrum.     Experiment.     If  a  beam  of  white  light 
from  the  sun  or  an  electric  arc  be  allowed  to  pass  through  a 
prism,  the  light  will  be  broken  up  into  Newton's  seven  colors 
of  the  solar  spectrum.     A  spectrum  is  a  color  or  series  of  colors 


LIGHT  349 

of  which  the  light  from  a  given  source  is  composed.  This 
breaking  up  of  white  light  into  prismatic  colors  is  called  dis- 
persion.  It  will  be  observed  from  Fig.  502  that  the  red  is 


FIG.  502.  —  Dispersion  of  White  Light 


least  refracted  and  the  violet  most.  The  colors  of  the  solar 
spectrum  are,  in  order  of  their  refraction:  red,  orange,  yellow, 
green,  blue,  indigo,  violet. 

We  have  seen  that  the  solar  spectrum  consists  of  seven  colors 
ranging  from  red  to  violet.  Every  substance  when  heated  to 
incandescence  has  its  own  characteristic  spectrum,  depending 
upon  the  physical  condition  of  the  body.  There  are  three 
kinds  of  spectra,  as  shown  in  Figs.  503,  504,  505.  The  first  is 
a  spectrum  of  the  sun,  showing  the  dark  bands  characteristic 
of  the  solar  spectrum.  The  second,  Fig.  504,  is  a  continuous 
spectrum  formed  by  light  from  the  electric  arc.  The  third 
is  very  appropriately  called  a  bright-line  spectrum.  The 
characteristics  of  the  three  kinds  of  spectra  will  be  discussed 
more  fully  in  a  later  topic. 

521.  The  Rainbow.  One  of  the  most  familiar  and  striking 
examples  of  dispersion  is  that  seen  in  the  rainbow.  In 
order  to  see  a  rainbow  three  conditions  are  necessary:  (a) 
There  must  bo  drops  of  water  in  a  cloud  or  mist;  (b)  the  sun 
must  be^hiningjon  the  cloud;  and  (c)  the_eye  of  the  observer 
must  be  in  such  a  position  as  to  receive  the  refracted  light  from 
the  raindrop;  that  is,  the  observer  must  stand  with  his  back 
to  the  sun. 

A  rainbow  may  be  formed  experimentally  as  follows  :  Allow  a 
strong  beam  of  light  from  the  sun  or  an  electric  lantern  to  pass 
through  a  circular  opening  in  a  screen  and  fall  upon  a  spherical 


350 


HIGH  SCHOOL  PHYSICS 


flask  full  of  water,  Fig.  506.  The  flask  represents  a  large  drop 
of  water  in  which  the  light  is  both  refracted  and  reflected; 
that  is,  it  is  refracted  on  entering  the  flask  and  reflected  from 


FIG.  506 

the  rear  surface,  being  thus  thrown  back  upon  the  screen,  form- 
ing a  circular  band  of  color,  red  on  the  outside  and  violet  on  the 
inside.  This  colored  band  upon  the  screen,  formed  by  the  dis- 
placement of  white  light  by  the  spherical  flask,  is  somewhat 
analogous  to  the  formation  of  the  rainbow. 

There  are  two  rainbows,  the  primary  and  the  secondary, 
Fig.  507.    The  primary  bow, which  is  the  one  usually  observed, 

is  much  the  brighter  of  the  two 
and  lies  inside  the  secondary.  In 
the  primary  bow  the  red  is  on 
the  outside  and  the  violet  on  the 
inside.  '  The  secondary  bow  is  the 
fainter  of  the  two,  and  in  fact  is 
not  usually  seen  except  under  very 
favorable  conditions.  Its  colors 
are  reversed  as  compared  with 
those  of  the  primary,  the  violet 
being  on  the  outside  and  the  red  on  the  inside. 

Theories  explaining  the  formation  of  the  colors  of  the  rain- 
bow are  quite  complex  and  have  given  rise  to  no  little  discus- 


8 


FIG.  507 


Fig.  503.  Solar  Spectrum.  Crossing  this  spectrum  there  are  many 
dark  lines  \vhich  are  called  Frauenhofer  lines.  Such  a  spectrum  is  very 
appropriately  called  a  Dark  Line  Spectrum.  These  lines,  however,  are 
not  visible  under  ordinary  conditions  without  the  aid  of  a  spectroscope. 


Fig.  504.  Continuous  Spectrum.  The  colors  of  a  continuous 
spectrum  blend  one  into  the  other  without  any  dark  lines  occurring,  as 
in  the  case  of  the  spectrum  of  Fig.  503.  A  continuous  spectrum  is  due 
to  incandescent  solids,  such  as  the  carbons  of  the  electric  arc,  or  the 
glowing  filament  of  an  incandescent  lamp. 


Fig.  505.  Bright  Line  Spectrum.  A  bright  line  spectrum  is  formed 
by  the  light  from  an  incandescent  gas.  Each  metal,  for  example,  when 
in  a  volatile  condition  and  heated  to  incandescence  gives  rise  to  its  own 
characteristic  bright  line  spectrum,  the  above  being  that  of  sodium. 


LIGHT  351 

sion.  We  have  reason  to  believe  that  the  order  and  character 
of  the  colors  are  due  to  three  main  causes:  (a)  reflection,  (b) 
refraction,  (c)  dispersion,  and  in  some  cases  to  a  fourth  cause 
(d)  interference  phenomena.  (Supplement,  594.) 

522.  Continuous  Spectrum.     There  are  three  kinds  of  spec- 
tra: (a)  continuous,  (b)  bright-line,  and  (c)  dark-line.     A  con- 
tinuous spectrum  is  one  in  which  the  colors  blend  gradually  from 
one  into  the  other  without  any  break.     The  spectrum  from 
an    arc  lamp  is  continuous,  the  colors  grading  continuously 
from  red  to  violet.     An  incandescent  solid  gives  a  continuous 
spectrum.     The  spectrum  from  a  gas  flame,  or  a  candle  flame, 
or  the  flame  of  a  kerosene  lamp  are  in  all  cases  continuous, 
the  luminous  properties  of  such  flames  being  due  to  the  red- 
hot  solid  particles  which  they  contain.      Likewise  a  platinum 
wire  or  any  other  metal  heated  to  incandescence  gives  a  con- 
tinuous spectrum. 

523.  Bright-line    Spectrum.     A   bright-line  spectrum  is   one 
consisting  of  one  or  more  bright  lines.     A  bright-line  spectrum 
is  formed  from  an  incandescent  gas.     Thus  if  a  piece  of  sodium 
be  placed  in  the  flame  of  a  Bunsen  burner  and  the  yellow  light 
examined  by  means  of  a  spectroscope,  a  single  yellow  band  will 
appear.     This  is  a  bright-line  spectrum.     So  long  as  a  substance 
remains  in  the  state  of  an  incandescent  solid  it  gives  a  continu- 
ous spectrum;   the  moment,  however,  that  it  becomes  gasified 
and  incandescent,  it  gives  a  bright-line  spectrum. 

524.  Dark-line   Spectrum.     A  dark-line  spectrum  is  one  in 
which  dark  lines  appear  at  intervals  across  the  color  band  of 
which  the  spectrum  is  composed.     Such  a  spectrum  is  formed 
when  the  light  from  an  incandescent  solid  passes  through  that 
of  an  incandescent  gas.     The  solar  spectrum  is  a  dark-line  spec- 
trum.    It  is  true  that  it  appears  to  the  naked  eye  to  be  contin- 
uous.    If,  however,  the  solar  spectrum  be  examined  by  means 
of  a  spectroscope,  it  will  be  found  that  many  dark  lines  appear 
in  it,  as  shown  in  Fig.  503.     These  are  called  Fraunhofer  lines, 
after  Joseph  Fraunhofer,  a  German  scientist,  who  was  one  of 


352  HIGH   SCHOOL  PHYSICS 

the  first  to  count  and  describe  them.  The  fact  that  the 
sun's  spectrum  is  a  dark-line  spectrum  tells  us  that  its  light 
comes  from  an  incandescent  solid,  liquid,  or  gas  under  high 
pressure  surrounded  by  an  incandescent  gas  under  relatively 
Jow  pressure. 

H  525.  Spectrum  Analysis.  If  any  substance  in  the  condi- 
tion of  an  incandescent  gas  be  examined  by  means  of  a  spectro- 
scope, Fig.  508,  it  is  possible  to  determine  from  the  nature  of 
its  spectra  many  facts  regarding  the  character  of  the  substance. 


FIG.  508.  —  Spectroscope 

For  example,  suppose  that  we  wish  to  determine  if  there  is  any 
sodium  in  a  given  inorganic  substance.  Dip  a  platinum  wire 
into  the  substance  and  then  place  it  in  the  colorless  part  of  a 
Bunsen  flame;  the  salt  will  be  volatilized,  and  if  any  sodium 
be  present  a  distinct  yellow  color  will  be  imparted  to  the  flame. 
If  this  be  examined  by  means  of  a  spectroscope  the  presence  of 
even  the  most  minute  trace  of  sodium  will  reveal  itself  by  the 
appearance  of  a  yellow  band.  Thus  it.  is  possible  to  determine 
the  presence  of  1/14,000,000  gram  of  sodium. 

Also,  when  the  spectrum  of  the  sun  and  the  stars  are  exam- 
ined and  we  find  present  the  lines  that  are  characteristic  of 
sodium,  iron,  magnesium,  and  other  metals  we  take  for  granted 
that  these  metals  are  present  in  the  heavenly  bodies  from  which 
the  light  came. 


LIGHT  353 

526.  The  Invisible  Spectrum.     The  visible  spectrum  is  that 
which  is  included  between  red  and  violet,  about  one  octave  of 
color;  that  is,  from  red  making  395  trillion  to  violet  which 
makes  760  trillion  vibrations  per  second.     The  visible  spec- 
trum, however,  is  not  the  limit  of  the  dispersion  of  ether  waves 
which  may  be  secured  by  a  prism.     Beyond  the  red  is  a  series 
of  longer  waves  which  manifest  themselves  to  our  senses  in  the 
form  of  heat.     Below  the  violet  there  are  very  short  waves 
which  are  capable  of  great  chemical  activity.     The  invisible 
rays  beyond  the  red  are  called  the  infra-red;  those  beyond  the 
violet  are  called  the  ultra-violet. 

527.  Analysis   and   Synthesis  of  White  Light.     The  white 
light  of  the  sun  may  be  considered  as  made  up  of  many  colors, 
the  most  striking  of  which  are  the  seven  so-called  spectral 
colors  which  appear  when  white  light  is  dispersed  by  a  prism. 
The  question  naturally  arises:  Is  it  possible  to  combine  these 
seven  colors  so  that  they  may  give  us  again  white  light?     Sir 
Isaac  Newton  asked  himself  this  very  question  and  was  one 
of  the  first  to  answer  it  by  means  of  an  experiment.     He  first 
passed  a  beam  of  white  light  through  a  prism,  causing  it  to 
become  dispersed;  he  then  passed  the  dispersed  beam  through 
a. second  prism,  inverted  with  respect  to  the  first,  Fig.  509, 
and  found  that  the  colors  of  the  spectrum  were  combined  by 
the  second  prism  into  a  band  of  pure  white  light. 


FIG.  509  FIG.  510 

The  breaking  up  of  white  light  into  its  spectral  colors  is  called 
analysis  of  white  light;  the  combining  of  these  colors  is  called 
synthesis. 

528.  Chromatic  Aberration.  When  white  light  passes 
through  a  lens  two  things  occur:  (a)  it  is  refracted  and  (b)  it 


354 


HIGH   SCHOOL  PHYSICS 


Crown 


Flint 

FIG.  511 


is  to  a  certain  extent  dispersed;  that  is  it  is  broken  up  into  pris- 
matic colors.  This  dispersion  of  white  light  which  occurs  in 
a  lens  is  called  chromatic  aberration  and  is  illustrated  in  Fig. 
510.  The  violet  rays,  being  the  most  refrangible,  come  to  a 
focus  nearer  the  lens  than  do  those  of  the  red.  If,  therefore,  a 
white  card  be  placed  in  the  light  at  x  there  may  be  observed 
around  the  outer  edge  a  fringe  of  red;  if  the  card  be  placed  at 
y  there  will  be  seen  around  the  outer  edge  a  fringe  of  violet. 
This  fringe  of  color  constitutes  a  very  serious  defect  in  the  lens, 
especially  where  it  is  desired  to  produce  a  clear  image,  as  in 
the  case  of  the  microscope.  The  remedy  for  chromatic  aberra- 
tion lies  in  the  use  of  two  lenses,  one  concave  and  the  other 
convex,  of  different  kinds  of  glass  ground  so  as 
to  fit  closely  one  upon  the  other.  In  Fig.  511 
there  is  shown  an  achromatic  lens  consisting  of 
a  bi-convex  lens  of  crown  glass  and  a  plano- 
concave lens  of  flint  glass.  The  light  passing 
through  such  a  lens  is  brought  to  a  focus  with- 
out being  dispersed.  Lenses  of  this  type  are  used  in  the  objec- 
tive of  the  compound  microscope. 

529.  Mixing  Colors.  Experiment.  Since  color  is  a  sensa- 
tion, it  follows  that  the  mixing  of  colors 
is  nothing  more  than  the  mixing  of  sensa- 
tions. If  a  color  disc,  sometimes  known 
as  Newton's  disc,  Fig.  512,  be  rapidly 
rotated,  the  eye  will  receive  a  series  of  im- 
pressions, the  resultant  sensation  of  which 
will  be  caused  by  the  mixing  of  the  sev- 
eral sensations  due  to  the  different  colors 
on  the  disc.  Thus  if  the  disc  be  rotated 
the  eye  will  no  longer  see  yellow,  blue, 
green,  etc.,  but  will  see  in  their  stead  gray 
or  white,  or  whatever  the  resultant  color 
may  be. 
FIG.  512  530.  Complementary  Colors.  Any  two 


LIGHT 


355 


colors  which  when  mixed  produce  the  sensation  of  white  are 
called  complementary  colors.  A  complementary  color  disc  is 
shown  in  Pig.  513.  Those  colors  which  are  opposite  each 
other  on  the  disc  will,  on  being  mixed,  produce  white.  Thus 
yellow  and  dark  blue  are  complementary,  as  may  be  shown 
by  the  following  very  simple  experiment.  Place  a  yellow  and 
a  blue  strip  of  paper  a  few  inches  apart  on  the  table  and  then 


PURPLE 


/V33UO 

FIG.  513 


FIG.  514 


view  them  by  means  of  a  piece  of  glass  as  shown  in  Fig.  514. 
The  sensation  produced,  that  is,  the  resultant  color,  will  be 
neither  blue  nor  yellow,  but  white.  The  light  from  the  blue 
reaches  the  eye  by  passing  through  the  glass ;  that  from  the  yel- 
low by  reflection  from  the  glass.  Both  trains  of  light  waves 
thus  unite  and  give  rise  to  the  common  sensation  of  white. 

Those  colors  which  produce  the  sharpest  contrast  are  in 
general  complementary  to  each  other.  For  example,  red  and 
green  are  complementary  colors.  When  these  colors  are  brought 
near  together  the  red  appears  redder  and  the  green  greener. 
Thus  the  red  rose  appears  redder  when  seen  against  the  back- 
ground of  green  leaves  than  it  otherwise  would.  Blue  also 
appears  bluer  when  placed  adjacent  to  a  yellow  field. 

531.  Mixing  Pigments.  Experiment.  We  have  just  learned 
that  when  the  colors  (sensations)  blue  and  yellow  are  mixed 
they  produce  white.  Now,  however,  if  yellow  and  blue  pig- 


356  HIGH  SCHOOL  PHYSICS 

ments  be  mixed,  in  the  sense  in  which  the  painter  mixes  colors, 
the  resulting  color  will  not  be  white,  but  green.  This  can 
easily  be  shown  by  mixing  yellow  and  blue  pigments  from  a 
set  of  water  colors. 

The  effect  of  mixing  pigments  can  also  be  shown  by  making 
on  the  blackboard  with  a  blue  crayon  a  broad  band  of  blue; 
then  over  the  blue  make  a  corresponding  band  of  yellow.  The 
mixture  of  blue  and  yellow  crayon  will  give  a  color  of  greenish 
tinge. 

^Mixing  pigments  then  produces  an  entirely  different  effect 
from  the  mixing  of  corresponding  colors.  Yellow  and  blue 
colors,  to  repeat,  produce  white;  yellow  and  blue  pigments 
produce  green.  The  reason  that  the  mixing  of  blue  and  yellow 
pigments  produces  green  is  because  the  blue  pigment  absorbs 
all  the  colors  of  white  light  except  blue  and  green,  and  the 
yellow  pigment  absorbs  all  but  the  red,  yellow,  and  green.  Now 
when  the  two  are  mixed  there  results  a  pigment  that  absorbs 
every  color  but  green,  which  is  reflected.  In  a  similar  manner 
we  may  explain  the  resulting  color  due  to  mixing  any  number 
of  pigments.  If,  for  example,  we  should  take  .a  combination  of 
pigments  of  such  a  nature  that  the  mixture  would  absorb  all 
the  colors  of  white  light,  the  resulting  mixture  would  be  black. 

532.  The  Color  of  Bodies.  The  color  of  any  body  is  due  to 
the  character  of  the  light  which  it  reflects,  or  transmits.  If  it 
reflects  light  having  a  wave  length  of  about  0.0007  millimeter  it 
gives  rise  to  the  color  of  red,  and  so  on  throughout  the  color  scale. 
We  often  speak  of  an  object  as  being  painted  a  given  color,  as, 
for  example,  red.  What  is  really  done  is  to  put  upon  the  object 
a  pigment  which  has  the  property  of  absorbing  the  light  of  all 
colors  excepting  red,  or  green,  or  whatever  the  color  may  be. 
Also,  if  a  piece  of  glass  be  held  up  before  the  sunlight,  and  the 
light  which  passes  through  it  falls  upon  the  eye  and  we  receive 
the  impression  of  red,  we  say  that  the  glass  is  red.  It  is  red 
simply  because  it  has  the  property  of  absorbing  all  the  colors 
except  those  which  give  rise  to  the  sensation  of  red,  which  wave 


LIGHT  357 

length  its  transmits.  That  is,  the  glass  absorbs  all  other  waves 
and  transmits  only  those  that  produce  red. 

This  all  means  that  the  color  of  any  object  is  not  something 
that  resides  within  the  object,  but  is  a  sensation  having  its 
seat  within  the  brain  of  the  observer.  The  red  of  the  rose, 
for  example,  is  not  in  the  rose,  but  in  the  sensorium  of  the 
observer.  The  rose  simply  has  the  property  of  reflecting  those 
waves  which  give  rise  to  the  sensation  of  red. 

533.  Colors  Due  to  Thin  Films.  Experiment.  If  a  soap 
bubble  be  observed  in  the  sunlight,  brilliant  colors  will  be  seen 
shifting  rapidly  across  the  surface  of  the  bubble.  These  colors, 
due  to  thin  films,  are  caused  by  what  is  known  as  interference. 
This  can  best  be  explained  in  an  elementary  way  by  means  of 
Fig.  515.  Since  the  light  is  a  wave  mo- 
tion, it  follows  that  two  waves  may 
interfere  in  almost  exactly  the  same 
way  that  two  sound  waves  interfere. 
It  is  possible,  therefore,  that  two  light 
waves  may  be  superimposed  one  upon 
the  other  in  such  a  way  that  one  may 

exactly  neutralize  the  other.  If  the  light  be  white  light,  that 
is,  light  consisting  of  the  seven  prismatic  colors,  and  one  color 
be  cut  out,  due  to  interference,  then  the  remaining  colors  of 
the  spectrum  will  appear.  Consider  a  band  of  light,  ab,  as 
falling  upon  a  thin  film,  AB.  Part  of  this  light  is  reflected 
and  part  passes  through  to  the  second  face  of  the  film  and  is 
then  reflected.  Now  if  it  happens  that  a  part  of  the  wave 
train  a  which  emerges  at  c  should  unite  with  the  reflected  part 
of  6  in  opposite  phase,  then  interference  will  occur. 

This,  in  general,  is  the  explanation  of  the  brilliant  bands  of 
color  which  occur  in  the  case  of  a  soap  film.  The  shifting  of 
these  bands  is  due  to  the  fact  that  the  film  is  constantly  chang- 
ing its  thickness.  Other  illustrations  of  interference  are  seen 
in  the  bright  colored  bands  which  appear  when  a  film  of  oil 
spreads  out  over  the  surface  of  water;  also  the  bright  bands 


358  HIGH  SCHOOL  PHYSICS 

which  appear  due  to  cracks  in  ice,  or  in  other  crystalline  sub- 
stances, illustrate  interference  effects. 

EXERCISES  AND   PROBLEMS   FOR  REVIEW 

t     1.   Define  light.     Wherein  do  light  waves  differ  from  sound  waves? 

2.  Compare  (a)  the  velocity  of  light  with  that  of  sound;    (b)  the 
velocity  of  light  in  a  vacuum  with  that  in  air;   (c)  velocity  in  air  with  that 
in  glass. 

3.  It  is  said  to  take  light  fifty-four  and  one  half  years  to  travel  from 
the  North  star  to  the  earth.     How  far  away  is  the  North  star? 

4.  The  star  Arcturus  is  600,000,000,000,000  miles  from  the  earth. 
Suppose  that  this  star  were  suddenly  extinguished,  how  long  would  it  be 
before  astronomers  could  detect  the  fact? 

6.    Make  a  drawing  to  illustrate  the  umbra  and  the  penumbra  in  the 
formation  of  shadows. 

6.  Explain  why  images  through  small  apertures  are  inverted.     What 
is  meant  when  we  say  that  such  images  are  perverted? 

7.  In  the  case  of  images  formed  through  small  apertures,  how  is  the 
intensity  of  illumination  affected  by  moving  the  source  of  light  toward  the 
aperture?     How  is  the  intensity  of   illumination   affected   by  increasing 
the  size  of  the  aperture?     What  effect  does  this  have  on  the  distinctness 
of  the  image? 

8.  An  image  is  formed  by  a  plane  mirror.    What  is  the  relation  of  the 
image  to  the  object  with  respect  to  distance  from  mirror?     Is  the  image 
real  or  virtual? 

9.  If  a  person  walk  toward  a  plane  mirror  with  a  velocity  of  8  ft.  per 
second,  with  what  velocity  does  he  approach  his  image? 

10.  Define  and  illustrate  by  drawing  with  reference  to  a  spherical 
mirror  the  following  terms:    (a)  Center  of  curvature;    (b)  vertex;    (c) 
principal  axis;    (d)  principal  focus;    (e)  secondary  axis. 

11.  Where  must  an  object  be  placed  with  reference  to  the  focus  of  a 
spherical  mirror  in  order  that  the  image  be  real  and  (a)  larger  than  the 
object?     (b)  Smaller  than  the  object? 

12.  In  what  two  positions  with  reference  to  spherical  mirrors  may  an  ob- 
ject be  placed  so  that  the  image  is  virtual?   Make  drawing  to  illustrate  each. 

13.  Define  and  illustrate  refraction.     Explain  how  light  is  refracted 
with  reference  to  the  normal  when  it  passes  (a)  from  a  rare  to  a  dense 
medium;   (b)  from  a  dense  to  a  rare  medium. 


LIGHT  359 

14.  A  man  standing  on  the  bank  of  a  stream  wishes  to  spear  a  fish  which 
lies  in  the  water  below  him.     Should  he  strike  a  little  high  or  a  little  low? 
Illustrate  by  diagram. 

15.  Define  index  of  refraction.     What  does  it  mean  when  we  say  that 
the  index  of  refraction  of  water  is  ^?     What  is  the  velocity  of  light  in 
water? 

16.  Considering  the  index  of  refraction  of  crown  glass  to  be  1.5,  what 
is  the  velocity  of  light  in  crown  glass? 

17.  What  is  a  convex  lens?     What  is  its  effect  on  parallel  rays  of 
light?     Name  and  illustrate  by  drawing  the  three  classes  of  convex  lenses. 

18.  What  is  a  concave  lens?  What  is  its  effect  on  parallel  rays  of  light? 
Name  and  illustrate  the  three  classes  of  concave  lenses. 

19.  Where  must  an  object  be  placed  with  reference  to  the  focus  of  a 
convex  lens  in  order  that  the  image  be  real  and  (a)  smaller  than  the  object? 
(b)  same  size  as  the  object?   (c)  larger  than  the  object? 

20.  Make  drawing  to  illustrate  the  simple  microscope. 

21.  Make  drawing  to  illustrate  cross  section  of  the  human  eye.     Name 
and  explain  the  function  of  each  part. 

22.  Define  and  illustrate  visual  angle.     Explain  the  relation  of  the 
apparent  size  of  an  object  to  the  visual  angle. 

23.  What  is  spherical  aberration  in  a  lens?     How  may  it  be  remedied? 

24.  What  is  chromatic  aberration?     How  may  it  be  remedied? 

25.  Define  color,  and  name  in  order  the  colors  of  the  solar  spectrum. 

26.  Suppose  that  a  person  were  in  a  balloon  above  the  clouds,  what 
shape  of  rainbow  might  it  be  possible  to  see? 

27.  The  velocity  of  light  is  300,000  km.  per  second,  and  the  wave  length 
of -red  light  is  0.0007  mm.     How  many  waves  of  light  of  this  color  will 
strike  the  eye  in  one  second? 

28.  If  the  waves  producing  the  sensation  of  red  were  all  absorbed  from 
sunlight,  what  color  would  objects  that  were  formerly  red  appear  to  have? 

29.  (a)  What  is  a  continuous  spectrum?   (b)  bright-line  spectrum?   (c) 
dark-line  spectrum?     Under  what  condition  is  each  formed? 

30.  The  luminosity  of  a  flame  of  a  kerosene  lamp  is  due  to  incandescent 
particles  of  carbon.     What  sort  of  a  spectrum  will  such  a  flame  give? 

31.  Compare  the  mixing  of  yellow  and  blue  colors  with  that  of  yellow 
and  blue  pigments. 

32.  What  are  complementary  colors?     Give  some  examples.     How  do 
complementary  colors  affect  each  other  when  placed  side  by  side? 


360  HIGH  SCHOOL  PHYSICS 

33.  Explain  the  occurrence  of  brilliant  bands  of  color  in  the  soap  film. 
What  causes  the  shifting  of  the  colors  in  the  film? 

34.  When  two  pieces  of  glass  are  pressed  together  colored  bands  some- 
times appear.    Explain. 

36.  Why  does  a  photographer  use  a  red  light  in  the  photographic  dark 
room? 

For  additional  Problems  and   Exercises,  see  Supplement. 


SUPPLEMENT 


NOTES 

534  (Art.  22).     It  is  important  to  note  that  the  International  Metric 
Standards  used  for  reference  are  not  the  Standards  of  the  Archives,  but  are 
the  International  Standard  Meter  and  Kilogram  kept  at  the  International 
Bureau,  at  Sevres,  near  Paris.     At  certain  times  our  National  Metric 
Standards  at  Washington  are  taken  to  Paris  and  compared  with  the 
International  Standards.    This  is  done  to  determine  that  no  variation  'in 
our  standards,  due  to  temperature  changes  or  other  causes,  has  occurred. 
This  comparison,  to  repeat,  is  made  with  the  International  Standards  kept 
in  the  International  Bureau. 

535  (Art.  25).     The  reason  for  defining  the  liter  in  terms  of  the  volume 
of  a  kilogram  of  air-free  distilled  water  at  4°  C.,  instead  of  defining  it  directly 
as  1000  cubic  centimeters,  is  because  of  the  convenience  in  calibrating 
glass  flasks  and  similar  vessels.     It  would  not  be  an  easy  matter  to  deter- 
mine the  volume  of  a  Florence  flask,  for  example,  by  direct  measurement; 
on  the  other  hand,  it  is  an  easy  matter  to  determine  its  volume  by  finding 
the  mass  of  water  which  it  will  contain  at  a  given  temperature. 

536  (Art.   37).     Accelerated    Motion    of    Bodies    Having    an    Initial 
Velocity.     In  our  discussion  of  accelerated  motion  in  the  text,  we  con- 
sidered only  the  simplest  cases  of  bodies  having  an  accelerated  motion 
starting  from  rest.     If  a  body  fall  from  rest  its  initial  velocity  is  zero  and 
its  velocity  at  the  end  of  any  instant  is 

v  =  gt 

If  a  body  be  thrown  downward  with  an  initial  velocity  v',  it  will  have 
at  the  end  of  any  given  interval  a  velocity  represented  by  the  equation 

v  =  vf  -f-  gt 
The  space  passed  over  during  any  interval  of  time  will  then  be 

'  s  =  v't  +  \g$ 
In  general  we  may  write 

v  =  v'  =t  at 
s  =  v't  =*=    aP 


362  HIGH  SCHOOL  PHYSICS 

EXERCISES.  1.  Suppose  that  a  sled  start  from  rest  on  a  hillside  and 
move  downward  with  an  acceleration  of  3  ft.  per  second  per  second,  (a) 
What  will  be  its  velocity  at  the  end  of  10  seconds?  (b)  at  the  end  of  1 
minute? 

2.  Suppose  that  a  ball  on  an  incline  start  from  rest  and  roll  downward 
with  an  acceleration  of  4  ft.  per  second  per  second.     How  far  will  it  roll 
(a)  in  20  seconds?   (b)  in  1  minute? 

3.  If  the  ball  (problem  2)  be  given  an  initial  velocity  of  10  ft.  per  second, 
how  far  will  it  roll  in  10  seconds? 

4.  Suppose  that  the  ball  be  thrown  up  the  incline  with   an   initial 
velocity  of  30  ft.  per  second.     How  far  will  it  roll  in  5  seconds,  the 
acceleration  being  —  4  ft.  per  second  per  second? 

5.  A  body  starting  from  rest  falls  for  10  seconds.     Over  what  space 
will  it  pass  (a)  in  feet?    (b)  in  centimeters? 

6.  A  body  is  thrown  downward  with  an  initial  velocity  of  10  ft.  per 
second.     How  far  will  it  go  in  10  seconds? 

7.  A  body  is  thrown  upward  with  an  initial  velocity  of  4900  cm.  per 
second.     How  far  will  it  rise  in  3  seconds? 

637  (Art.  42).     The  unit   of   momentum   is   the   momentum   of   unit 
mass  having  unit  velocity.     In  the  C.G.S.  system  the  unit  of  momentum 
is  the  momentum  of  a  mass  of  one  gram  moving  with  a  velocity  of  one 
centimeter  per  second.     There  is  no  generally  accepted  name  for  this  unit, 
although  the  name  bole  was  proposed  by  the  Committee  of  the  British 
Association.    In  the  F.P.S.  system  the  unit  of  momentum  is  the  momen- 
tum of  a  mass  of  one  pound  having  a  velocity  of  one  foot  per  second. 

638  (Art.  45).     The  third  law  of  motion  expresses  the  fact  that  Ihe 
action  of  a  force  operating  between  two  bodies  is  dual  in  character;   that 
is,  the  force  always  acts  both  ways.     Thus,  if  we  push  on  a  body  with  a 
force  F,  the  body  pushes  back  with  an  equal  force  F'.     Now  force  may  be 

defined  as  F  =  ma  =  — '  in  which  v  is  the  change  of  velocity  in  the  time  t; 
as  also  F'  =  -—-'  The  t  is  the  same  in  both  cases  since  the  time  in  which 
the  force  acts  on  both  bodies  is  equal.  Now  since  F  =  F',  then  —  =  -r~  » 

and  therefore  mv  =  m'v'.  That  is,  when  any  mutual  action  takes  place 
between  any  two  bodies  the  momenta  generated  in  opposite  directions  are 
equal. 

639  (Art.  49).     Since  the  attraction  of  the  earth  (the  force  of  gravity) 
varies  for  different  places  on  the  earth's  surface,  it  would  seem  necessary 
to  define  the  unit  of  weight  with  reference  to  some  particular  place.     In 
Great  Britain  the  weight  of  a  pound  is  defined  as  the  force  with  which 


SUPPLEMENT 


363 


the  earth  attracts  a  pound  mass  at  sea  level,  45°  north  latitude.  In  this 
country  (U.  S.)  no  specific  definition  has  ever  been  made,  the  English 
definition  being  generally  accepted.  The  slight  variation  of  a  force  of  a 
pound  due  to  the  variation  of  gravity  is,  for  all  ordinary  measurements, 
practically  negligible. 

540  (Art.  51).     In  gravitational  units  the  force  of  a  pound,  for  example, 
is  the  force  with  which  the  earth  attracts  a  pound  mass.     Absolute  units, 
on  the  other  hand,  are  measured  in  terms  of  unit  mass  and  unit  accelera- 
tion; that  is,  F  =  ma.     Now  if  a  pound  mass  were  allowed  to  fall  freely 
in  a  vacuum,  its  acceleration  at  sea  level  would  be  about  32.16  feet  per 
second  per  second,  and  in  a  like  manner,  a  mass  of  one  gram  would  have 
an  acceleration  of  about  980  centimeters  per  second  per  second.     We  say 
then  that  the  force  of  a  pound  measured  in  gravitational  units  is  equiva- 
lent to  about  32  absolute  units  (poundals),  and  that  a  force  of  one  gram 
in  gravitational  units  is  equivalent  to  about  980  absolute  units  (dynes). 

541  (Art.  52).     In  a  striqt  scientific  sense,  a  force  is  fully  described 
when  we  know  four  things  about  it;  namely,  (a)  its  point  of  application, 
(b)  its  magnitude,  (c)  its  direction,  and  (d)  its  sense.     In  ordinary  language 
the  word  direction  means  both  direction  and  sense.     Thus  a  stone  falls  to 
the  ground.     We  say  in  ordinary  language  that  the  direction  of  its  motion  is 
down.     In  scientific  language  we  would  describe  the  fall  of  the  stone  by  say- 
ing that  its  direction  is  vertical  and  its  sense  down.     In  an  elementary  text, 
however,  it  is  not  considered  necessary  to  introduce  this  additional  term. 

542  (Art.  58).     To  Find  the  Resultant  when  more  than  Two  Com- 
ponents are  Given.     When  more  than  two  components  are  given,  Fig. 
516,  we  proceed  to  find  the  resultant  as 

follpws:  First,  we  select  any  two  com- 
ponents, as  AB,  AC,  and  complete  the 
parallelogram  ABDC,  and  draw  the  diag- 
onal AD.  With  this  line  AD,  and  the 
next  component  AE,  complete  a  new 
parallelogram  ADFE.  Continue  this 
process  until  all  the  components  have 
been  taken.  The  last  diagonal,  which 
in  this  case  is  AF,  represents  the  result- 
ant of  all  the  components.  It  makes  no 
difference  in  what  order  the  components 
are  taken,  the  resultant  will  be  the  same  in  every  case,  both  in  direction 
and  magnitude. 

543  (Art.  59).     Resolution  of  Forces.     In  considering  the  subject  of 
resolution  of  forces,  two  important  cases  arise,  as  illustrated  in  the  follow- 
ing examples: 


FIG.  516 


364 


HIGH  SCHOOL  PHYSICS 


(a)  Given  the  resultant  and  the  magnitude  and  direction  of  one  of  the 
components  to  find  the  other.  Suppose,  for  example,  a  resultant  force 
of  100  dynes  is  due  to  two  components,  one  of  which  has  a  magnitude  of 
60  dynes  and  makes  an  angle  of  25°  with  the  resultant,  and  we  desire  to 
find  the  direction  and  magnitude  of  the  other  component.  Lay  off  line 
AB,  Fig.  517,  equal  to  60  units  in  length,  representing  60  dynes.  Then 
from  the  point  A  lay  off  AD,  the  resultant,  100  units  in  length,  making 
an  angle  of  25°  with  AB.  Draw  line  BD.  Now  draw  AC  equal  and 
parallel  to  BD.  The  line  AC  represents  in  direction  and  magnitude  the 
component  sought. 


FIG.  517 


FIG.  518 


(b)  Given  the  resultant  and  direction  of  the  components  to  find  the 
magnitude  of  each.  Example.  Two  component  forces  produce  a  result- 
ant force  of  20  pounds.  The  angle  between  the  resultant  and  one  of  the 
components  is  25°  and  the  other  45°.  It  is  desired  to  find  the  magni- 
tude of  the  components.  Draw  line  Ab,  Fig.  518.  From  point  A  draw 
AD  representing  the  magnitude  and  direction  of  the  resultant.  Let  this 
line  be  20  units  in  length,  making  an  angle  of  25°  with  Ab.  Now  draw  Ac 
making  an  angle  of  45°  with  the  resultant  AD.  From  D  draw  DB  parallel 
to  Ac,  and  DC  parallel  to  Ab.  Lines  AB  and  AC  represent  the  direction 
and  magnitude  of  the  components. 

644  (Art.  64) .  According  to  Newton's  law  of  universal  gravitation  any 
particle  of  mass  m  is  attracted  by  any  other  particle  of  mass  m',  with 
a  force  F,  directly  proportional  to  the  product  of  the  masses  mm',  and 
inversely  proportional  to  the  square  of  the  distance  between  the  particles. 
This  is  expressed  by  the  law 


F  =  k 


mm' 


in  which  k  is  a  constant  called  the  constant  of  gravitation.  This  constant 
k  represents  the  force  with  which  two  particles,  each  of  unit  mass,  attract 
each  other  when  at  unit  distance  apart.  The  value  of  k  has  to  be  deter- 
mined by  experiment,  and  its  numerical  value  depends  upon  the  units  of 
measurement  adopted.  What  can  be  directly  observed  is,  of  course, 


SUPPLEMENT  365 

not  the  force  itself,  but  the  acceleration  which  it  produces.     Now  taking 
g  =  980,  we  find  in  C.G.S.  units  that  k  =  0.000  000  067. 

Example.  The  masses  of  two  homogeneous  spheres  are  10  and  30 
grams  respectively.  The  distance  between  their  centers  is  30  centimeters. 
Find  the  force  in  dynes  with  which  the  two  bodies  attract  each  other. 

Solution :       F  =  k  ^  =  0.000  000  067  X  10  X  30/900  =  0.000  000  022 
dyne. 

545  (Art.  66).     According  to  Newton's  law  of  gravitation  the  weight 
of  a  body  above  the  surface  of  the  earth  will  be  inversely  proportional  to 
the  square  of  its  distance  from  the  center  of  the  earth.     Since  the  mass  of 
the  earth  and  the  mass  of  the  body  remain  constant,  we  may  say  that  the 
weight  of  a  body  at  the  surface  is  to  its  weight  above  the  surface  as 
the  square  of  its  distance  from  the  center  is  to  the  square  of  the  radius  of 
the  earth;  that  is, 

w  :  w'  —  d'2  :  d? 

Example.  A  body  weighs  100  Ibs.  at  the  surface  of  the  earth.  What 
will  be  its  weight  1000  miles  above  the  surface  of  the  earth?  Solution: 
100  :  x  =  50002  :  40004.  Hence  x  =  64  Ibs. 

If  the  earth  were  uniform  in  density  the  weight  of  a  body  below  the 
surface  would  be  directly  proportional  to  its  distance  from  the  center. 
It  is  customary  in  elementary  texts  to  give  problems  illustrating  this  law 
of  variation  below  the  surface,  it  being  taken  for  granted  that  the  earth 
is  of  uniform  density.  Since  the  density  of  the  earth,  however,  increases 
from  the  surface  to  the  center,  such  an  assumption  is  not  justified . 

The  reason  why  a  body  below  the  surface  of  the  earth  weighs  less  than 
at  the  surface  is  because  there  is  less  mass  between  it  and  the  center  of  the 
earth  to  attract  it.  It  can  be  shown  mathematically  that  if  the  earth 
consisted  of  a  hollow  sphere  and  a  ball  were  placed  anywhere  within  the 
interior,  it  would  be  attracted  equally  in  all  directions,  that  is  to  say,  it 
would  remain  in  position  wherever  placed. 

546  (Art.  78).     In  the  mathematical  derivation  of  the  equation  for  the 
pendulum,  T  =  Tr\/l/g,  the  assumption  is  made  that  the  arc  swept  out 
by  the  pendulum  is  practically  a  straight  line.     Now  this  is  true  within 
the  limits  of  error  permissible  in  this  derivation  when  the  amplitude  of 
the  arc  is  not  over  3  degrees;  that  is,  when  the  entire  arc  subtends  an 
angle  of  5  or  6  degrees. 

547  (Art.  92).     The   derivation   of    the    equation   for   kinetic    energy 
F  =  \m^  is  as  follows:    If  a  mass  m  be  acted  upon  by  a  force  F,  for  a 
time  t,  during  which  it  receives  an  acceleration  a,  it  will  pass  over  a  space 


366 


HIGH  SCHOOL  PHYSICS 


and  acquire  a  velocity 


=  at 


Now  energy  is  numerically  equal  to  work;    hence  we  may  write 

W  =  Fs  =  mas  =  %maztz  = 


It  will  be  observed  that  in  deriving  this  equation  for  kinetic  energy,  we 
started  with  an  equation  which  expressed  force  in  absolute  units,  F  =  ma. 
It  is  for  this  reason  that  the  equation  K.E.  =  ^mv2  gives  results  in  absolute 
units  (foot  poundals  or  ergs)  . 

648  (Art.  100).     In  speaking  of  the  reduction  of  compound  machines 
to  one  of  the  six  simple  types,  we  use  the  term  mechanical  machine  because, 
using  the  term  machine  in  a  broad  sense,  there  are  some  machines  which 
cannot  be  reduced  to  any  one  of  the  six  simple  machines.     An  example 
of  this  is  the  electric  transformer.     This  instrument  is  in  a  sense  a  machine 
for  the  transformation  of  electrical  energy  of  high  potential,  say,  to  low 
potential.     It,  however,  cannot  be  called  a  mechanical  machine. 

649  (Art.  108).     The  word  pressure  in  many  texts  is  used  as  synony- 
mous with  force.     When   used   in   an  accurate  scientific  sense,  however, 
pressure  always  means  force  per  unit  area;  that  is,  for  example,  force  in 
pounds  per  square  inch  or  square  foot,  or  grams  or  dynes  per  square  centi- 
meter.    In  this  text  pressure  is  always  used  to  mean  force  per  unit  area. 

560  (Art.  113).  By  the  term  center  of  figure,  as  used  in  connection  with 
the  equation  F  =  AHD,  we  mean  the  center  of  gravity  (centroid)  of  the 
area  of  the  surface  pressed  upon.  Thus,  if  the  surface  pressed  upon  be  a 
rectangle,  its  centroid  is  at  the  intersection  of  its  diagonals;  if  the  surface 
pressed  upon  be  a  triangle,  its  centroid  lies  at  the  point  of  intersection  of 
its  median  lines;  if  the  surface  pressed  upon  be  a  circle,  its  centroid  lies 
at  its  center,  etc. 


FIG.  519 


SUPPLEMENT 


367 


651  (Art.  118).  The  Turbine  Water  Wheel.  This  is  a  type  of  water 
wheel  somewhat  similar  in  principle  to  that  of  the  water  motor.  The 
wheel  is  placed  on  a  vertical  shaft.  Water  from  the  dam  is  conducted 
through  a  cylindrical  tube,  or  flume,  to  a  penstock,  which  surrounds  the 
stationary  iron  case  containing  the  turbine,  T  of  Fig.  519.  Water  enters 
the  turbine  case  through  the  openings  marked  A,  B,  C,  striking  against 
the  blades  of  the  wheel  and  then  discharging  down  through  the  center. 
Accompanying  Fig.  519  there  is  a  cross  sectional  diagram  of  the  wheel, 
illustrating  the  direction  of  the  inflow  of  the  water  at  S. 

552.  Hydraulic  Elevator.  An  application  of  the  transmission  of  energy 
by  water  power  under  pressure  is  found  in  the  hydraulic  elevator.  There 

are  two  common  types  of  such  elevators,  one  of  which  is    

shown  in  Fig.  520.  When  the  piston  P  is  forced  down- 
ward, for  example,  by  the  pressure  of  the  water,  the  ele- 
vator cage  rises.  Since  there  are  four  ropes  or  cables 
attached  to  the  movable  pulley  system,  it  follows  that 
when  P  moves  1  foot  the  cage  will  move 
4  feet.  Thus,  if  P  were  to  move  down- 
ward 10  feet,  the  cage  would  move  upward 
a  distance  of  40  feet. 

Sometimes  the  cage  is  fastened  directly 
upon  a  shaft  which  moves  in  a  deep  pit, 
Fig.  521.  Passing  through  the  cage  is  a 
cord  which  operates  a  two-way  valve, 
Fig.  522.  When  c  is  pulled  upward,  valve 
v  opens  and  v'  closes,  admitting  water  to 
the  pit  from  the  high  pressure  main, 
and  thus  causing  the  elevator  to  ascend; 
when  c  is  pulled  downward  valve  v  is 
closed  and  v'  is  opened  and  the  water 
flows  from  the  pit  into  the  waste  pipe,  allowing  the  ele- 
vator to  descend. 

The  general  principle  of  the  opera- 
tion of  a  two-way  valve  is  illustrated 
in  Fig.  522.  As  the  valve  is  set  in  the 
figure,  water  flows  from  the  elevator 
shaft  through  ^the  pipe  B  into  t}ie  waste 
pipe  F.  When  the  arm  D  is  moved 
downward  through  an  angle  of  90°,  thus  rotating  valve 
E  in  a  counter-clockwise  direction,  the  openings  in  the 
valve  E  connect  the  pipes  A  and  B,  thus  allowing 
water  from  the  high  pressure  main  A  to  enter  the  elevator  shaft  through  B. 


FIG.  520 


FIG.  521 


FIG.  522 


368 


HIGH   SCHOOL  PHYSICS 


FIG.  523 


653.  Hydraulic  Ram.  The  hydraulic  ram  is  an  apparatus  for  elevating 
water  to  a  height  greater  than  its  source.  The  condition  for  the  operation 
of  the  ram  is  that  there  be  a  supply  of  running  water.  The  water  flows 
through  a  pipe  p  and  out  through  a  valve  v,  Fig. 
523.  As  the  speed  of  the  stream  through  the  pipe 
increases,  valve  v  suddenly  closes,  thus  causing 
the  water,  because  of  the  momentum,  to  force  its 
way  for  an  instant  through  the  valve  V  into  the 
chamber  C.  The  water  in  the  pipe  p  now  re- 
bounds, relieving  the  pressure  on  the  valve  v, 
\  k-nrV  which  falls  by  its  own  weight,  thus  opening  the 

\=i^r/  ^         orifice  at  the  end  of  the  pipe.     The  process  is 
\— ^—[  vfergf      again  repeated,  and  more  water  is  forced  into  the 
chamber  C.     The  air  cushion  in  C  tends  to  pro- 
duce a  steady  flow  in  the  vertical  pipe  P. 

554  (Art.  135,  Exp.  2}.     In  order  to  make  this 
experiment  work  it  is  necessary  to  have  a  funnel 

the  edges  of  which  fit  closely  to  the  glass.     A  little  vaseline  rubbed  around 
the  edge  of  the  funnel  will  facilitate  the  formation  of  an  air-tight  joint. 

Experiment  3.  The  Magdeburg  Hemispheres  furnish  material  for  two 
interesting  problems.  One  is  to  find  the  total  force  upon  the  surface  of  the 
sphere,  the  other  is  to  find  the  force  required  to  pull  the  hemispheres  apart. 
The  force  required  to  pull  the  hemispheres  apart  is  equal  to  the  force 
exerted  on  the  area  of  a  great  circle  of  the  sphere.  Thus  it  appears  that 
the  total  force  exerted  upon  the  surface  of  this  sphere,  due  to  atmospheric 
pressure,  and  the  force  required  to  pull  the  hemispheres  apart  are  two 
entirely  different  propositions. 

One  of  the  first  to  experiment  with  these  hemispheres  was  Otto  von 
Guericke  (1602-1686),  a  scientist  and  burgomaster  of  Magdeburg,  Ger- 
many. Guericke  prepared  a  pair  of  hemispheres  having  a  diameter  of  1.2 
feet.  He  then  thoroughly  exhausted  the  air  and  invited  the  Emperor, 
Ferdinand  II,  to  witness  the  pulling  of  the  spheres  apart.  He  hitched 
horses  to  each  hemisphere,  increasing  the  number  to  sixteen  before  the 
spheres  were  pulled  apart.  In  this  respect  he  played  a  trick  upon  his  won- 
dering auditors,  because,  as  we  now  know  well,  and  as  he  no  doubt  knew, 
the  spheres  could  have  been  pulled  apart  by  fastening  one  side  of  the 
apparatus  to  a  stake  or  a  tree  and  fastening  the  horses  to  the  other  side, 
in  which  case  only  eight  horses  would  have  been  required.  The  experi- 
ment, however,  would  not  have  been  so  striking. 

565  (Art.  148).  In  Fig.  524  there  is  shown  in  outline  the  mechanism 
of  a  metallic-valve  air  pump.  The  metallic  valve  fits  very  accurately 
into  a  groove,  and  is  operated  by  the  motion  of  the  rod  C,  which  in  turn  is 


SUPPLEMENT 


369 


moved  up  and  down  by  the  motion  of  the  piston  P.     This  type  of  pump 
is  illustrated  by  the  usual  laboratory  pump. 


FIG.  524 


556.  The  Automatic  Air  Brake.  One  of  the  most  important  com- 
mercial applications  of  compressed  air  is  that  made  use  of  in  the  Westing- 
house  air  brake,  now  used  on  nearly  all  steam  and  electric  cars.  The 
principle  upon  which  the  air  brake  works  is  illustrated  in  the  diagram, 
Fig.  525.  A  compression  pump  on 
the  engine  supplies  air  to  the  re- 
ceiver R  through  the  pipe  P  under 
a  pressure  of  about  70  pounds  to 
the  square  inch.  The  receiver  R 
connects  with  the  cylinder  I  and 
with  the  pipe  P  through  a  triple 
valve  V.  While  the  pressure  is  on 
P  the  valve  V  opens  in  such  a  way 
that  there  is  direct  communication 
between  P  and  R.  When  the  pres-  FIG.  525 

sure  on  P  falls,  due  to  the  opera- 
tion of  a  lever  by  the  engineer  or  motorman,  or  by  the  accidental  break- 
ing of  the  connections,  the  compressed  air  in  R  operates  the  valve  V  in 
such  a  way  as  to  shut  off  connections  between  R  and  P  and  to  open  con- 
nections between  R  and  7.  The  brake  rod  B  is  then  driven  powerfully 
forward,  forcing  the  brake  against  the  wheels.  When  the  pressure  is 
again  turned  on  in  P,  valve  V  opens  in  such  a  way  as  to  allow  the  air  in 
7  to  escape,  and  the  spring  then  drives  the  piston  to  the  right,  thus  pulling 
the  brake  from  the  wheels. 


370 


HIGH   SCHOOL  PHYSICS 


The  Gas  Meter.     The  gas  meter  is  a  device  which  operates  under  the 
pressure  of  the  gas  in  the  city  mains,  and  thus  registers  automatically  in 
cubic  feet  the  quantity  of  gas  passing  through  it.     It  consists  essentially 
of  a  double  bellows,  as  shown  in  Fig.  526.      Gas  enters  through  the  pipe  P 
and  passes  down  into  chambers  A  and  C,  push- 
ing the  bellows  to  the  right.     This  forces  the 
gas  in  chambers  B  and  D  out  through  the  deliv- 
ery pipe  Q.     Now  the  motion  of  the  bellows  to 
the  right  causes  the  valve  V  to  move  to  the 
left,  thus  closing  the  opening  into  A  and  open- 
ing that  into'  D.     The  gas  now  flows  in  on  the 
right  of  valve  V,  and  the  bellows  moves  to  the 
left,  pushing  the  air  in  A   and  C  out  through 
the  pipe  Q.     When  the  bellows  is  moved  to  the 
left  the  valve  V  again  slides  to  the  right  and 
the  process  is  repeated.     The  valve  V  connects 
not  only  with  the  bellows,  but  also  with  a  train 
FIG.  526  of  wheels  which  register  on  a  set  of  dials  the 

number  of  cubic  feet  of  gas  consumed. 

657.   The  Dirigible  Balloon.     A  dirigible  balloon  consists,  in  general, 
of  a  cigar-shaped  receptacle  for  holding  the  gas,  below  which  is  suspended 


FIG.  527.  —  Zeppelin  Dirigible  Balloon 

the  car  for  the  accommodation  of  the  driving  engine  and  passengers,  Fig. 
527.  Propulsion  is  obtained  by  means  of  the  rotation  of  fan-like  propellers. 
On  the  dirigible  shown  in  Fig.  527  there  are  four  propellers  arranged  in 


SUPPLEMENT  371 

pairs,  one  pair  being  placed  above  each  car.  These  balloons  are  usually 
supplied  with  two  sets  of  rudders  operating  at  right  angles  to  each  other, 
one  designed  to  elevate  or  depress  the  balloon,  and  the  other  designed  to 
move  it  to  the  right  or  left. 

Of  the  various  types  of  dirigibles  those  that  were  constructed  by  Count 
Zeppelin  of  Germany  are  the  most  famous.  Zeppelin's  air  ship  consisted 
of  a  cylindrical  sac  more  than  300  feet  in  length,  containing  as  many  as 
17  compartments,  each  filled  with  a  gas  lighter  than  air.  Rigidity  was 
secured  by  means  of  a  metal  framework,  the  metal  used  being  mainly 
aluminum.  His  first  balloon  had  a  capacity  of  over  400,000  feet.  As  can 
be  imagined,  such  an  enormous  piece  of  mechanism  proved  unwieldy,  and 
after  a  few  trials  was  wrecked.  Zeppelin,  with  dogged  perseverance,  built 
five  different  balloons.  In  1909  his  air  ship,  known  as  "Zeppelin  No.  IV," 
made  a  record  flight  of  1100  kilometers  (684  miles)  in  thirty-eight  hours. 
This  balloon  was  destroyed  in  a  storm,  and  the  same  fate  befell  his  fifth 
attempt  in  1910. 

The  main  outcome  of  Zeppelin's  experiments  has  'been  to  prove  the 
impracticability  of  the  dirigible  balloon  of  the  rigid  type.  If  the  diri- 
gible balloon  is,  in  the  future,  to  be  of  any  use  to  man,  it  will  undoubtedly 
be  of  the  so-called  "  supple  "  type. 

558.  The  Aeroplane.  Aviation  is  the  art  of  lifting  and  propelling 
through  the  atmosphere  a  body  "  heavier  than  air  "  by  utilizing  the  resist- 
ance offered  by  the  air  itself  to  the  movement  of  the  body.  For  centuries 
man  has  attempted  to  emulate  the  flight  of  birds,  which  are  in  a  sense 
heavier-than-air  machines.  The  apparatus  that  he  has  used  in  attempting 
to  fly  may  be  classified  under  three  heads:  (a)  Those  which  are  propelled 
by  flapping  wings,  in  imitation  of  birds;  (b)  those  which  depend  for  their 
propulsion  through  the  air  upon  screw-propellers  alone;  and  (c)  those 
which  depend  for  their  support  upon  wing- 
like  surfaces,  and  for  their  horizontal  mo- 
tion upon  the  screw-propeller.  ^^^  Wind 

The  soaring  bird  and  the  flying  kite 
were  the  natural  forerunners  of  the  modern 
aeroplane.  The  operation  of  the  aeroplane 
may  be  best  understood  by  considering  the 
phenomena  of  the  flying  of  a  kite,  Fig.  528. 
Three  forces  act  upon  the  kite.  One  is  its 
weight  downward;  another  is  the  force  c  FIG.  528 

in  the  cord  which  keeps  it  in  an  oblique 

position;  and  the  third  is  the  force  of  the  wind,  a  component  of  which  acts 
upward  upon  it.  Now  the  aeroplane  may  be  regarded  as  a  kite  which  is 
self-propelling.  As  it  is  driven  through  the  atmosphere  by  means  of  the 


372 


HIGH  SCHOOL  PHYSICS 


rotation  of  its  screw-propeller,  the  air  exerts  a  force  which  is  sufficient 
to  support  it.  Like  the  dirigible  balloon  it  is  directed  to  the  right  or  left, 
up  or  down,  by  means  of  rudders.  Fig.  529  was  taken  from  a  snap-shot 
photograph  of  a  race  between  an  aeroplane  and  an  automobile.  It  is  in- 
teresting to  note  that  while  the  automobile  shows  evidence  of  great  speed, 
yet  the  wheels  appear  to  be  stationary,  the  spokes  showing  distinctly. 
This  is  explained  by  the  fact  that  the  picture  is  the  result  of  a  snap  shot, 
the  camera  giving  an  instantaneous  view  of  both  aeroplane  and  automobile. 


FIG.  529.  —  Aeroplane  and  Automobile  Racing 


In  all  trials  in  which  prolonged  flights  have  been  accomplished  it  has 
been  found  that  a  speed  of  30  to  50  miles  per  hour  is  required.  Speed  is 
an  absolute  necessity,  for  the  heavier-than-air  machine  depends  upon  its 
speed  for  two  things:  first,  its  support  in  the  air,  and  second,  its  ability 
to  overcome  fluctuations  in  atmospheric  currents. 

It  is  worthy  of  note  that  navigation  of  the  air  by  means  of  the  aeroplane 
became  possible  as  soon  as  a  light  and  powerful  motor  was  developed. 
The  light  modern  gas  engine  and  the  aeroplane  appeared  almost  simul- 
taneously. The  problem  of  successful  navigation  of  the  air  depends  upon 
the  efficiency  of  the  balancing  and  propelling  appliances. 

559  (Art.  182).  Count  Rumford  (Benjamin  Thompson)  was  one  of  the 
most  interesting  characters  of  his  day.  He  was  born  in  Massachusetts 
in  1753.  He  went  to  England  during  the  Revolutionary  period,  and  later 
went  to  Germany,  where  he  settled  at  Munich,  in  the  employ  of  the  Elector 
of  Bavaria,  with  whom  he  acquired  great  influence.  During  the  super- 


SUPPLEMENT 


373 


vision  of  the  boring  of  some  brass  cannon,  he  observed  the  relation  between 
the  work  done  by  the  horse  driving  the  machinery  and  the  heat  developed 
by  the  boring  tool.  At  that  time  it  was  supposed  that  heat  was  a  fluid. 
Rumford  concluded  that  there  was  some  relation  between  the  motion  of 
the  particles  of  the  brass  and  the  heat  developed.  He  went  so  far  as  to 
measure  the  quantity  of  heat  given  off  in  the  boring  of  one  of  the  cannons, 
and  in  this  experiment  he  came  very  near  discovering  the  mechanical 
equivalent  of  heat. 

He  was  shown  many  honors  by  the  German  government.  He  was  made 
Minister  of  War,  and  on  the  occasion  of  his  receiving  his  title,  in  1790,  he 
chose  the  name  Rumford,  after  the  town  in  New  Hampshire  where  he  had 
resided  prior  to  leaving  New  England. 

560  (Art.  192).  Since  mercury  freezes  at  —  39°  C.,  and  consequently 
cannot  be  used  to  measure  temperature  below  this  point,  liquids  having 
lower  freezing  points,  such  as  toluene,  alcohol,  or  pentane,  have  to  be 
employed.  The  freezing  points  of  these  liquids  are:  toluene,  —  80°  C.; 
alcohol,  -  130°  C.;  pentane,  below  -  200°  C. 

661  (Art.  211).  Gay-Lussac's  law  is  frequently  referred  to  as  the  law 
of  Charles.  There  is  no  doubt  that  Charles,  who  was  a  contemporary  of 
Gay-Lussac,  knew  of  the  relation  expressed  by  the  law  prior  to  the  time 
of  its  publication  by  Gay-Lussac.  To  Gay-Lussac,  however,  belongs  the 
credit  of  working  out  the  law  and  first  submitting  it  to  publication. 

562  (Art.  220).     In  "performing  this  experiment  a  drying  tube  should 
be  placed  between  the  flask  and  the  air  pump  to  prevent  the  water  vapor 
from  the  flask  going  over  into  the  pump. 

563  (Art.  235).     A  very  good  freezing  mixture  consists  of  a  mixture  of 
2  parts  by  weight  of  ammonium  nitrate  and  1  part  of  ammonium  chloride. 

664  (Art.  239).  The  Commercial  Ice  Machine.  The  manufacture  of 
ice  depends  upon  the  principle  of  the  reduction  of  cold  by  evaporation  and 
expansion.  In  the  modern  refrigerating  plant,  ammonia  gas  is  condensed 

W 


W^ 

A 

I 

^Ill'-'lll 

g£ 

^        P  

FIG.  530 


374  HIGH  SCHOOL  PHYSICS 

into  a  liquid  by  means  of  a  powerful  pump.  This  liquid  ammonia,  which 
is  somewhat  heated  by  the  process  of  compression,  is  cooled  by  a  spray  W 
of  cold  water  which  plays  upon  the  pipes  through  which  it  passes.  The 
liquid  ammonia  is  allowed  to  expand  in  the  tube  A,  Fig.  530,  which  is  sur- 
rounded with  brine,  B.  The  expansion  of  the  liquid  ammonia  produces 
intense  cold,  the  brine  thus  being  lowered  to  a  temperature  of  —  10°  C. 
A  vessel  of  water,  F,  placed  in  this  tank  quickly  freezes.  The  cold  brine 
is  sometimes  pumped  to  the  various  parts  of  the  building  R,  thus  supplying 
the  low  temperature  necessary  for  cold  storage. 

Liquid  Air.  The  principle  of  the  production  of  liquid  air  does  not 
differ  materially  from  that  involved  in  the  production  of  cold  as  explained 
in  the  operation  of  the  ice  machine.  Liquid  air  is  now  made  in  large  quan- 
tities by  a  continuous  process  first  worked  out  by  Linde.  Air  is  compressed 
in  a  tank  under  a  pressure  of  about  200  atmospheres.  It  is  led  from  the 
reservoir  down  through  a  coil  of  pipe,  where  it  is  discharged  through  a  very 
small  aperture.  In  passing  through  the  aperture  it  expands  and  is  very 
much  cooled.  It  is  now  conducted  to  the  top  of  the  tank,  passing  on  its 
way  upward  over  the  coils  in  which  it  was  compressed.  This  cool  air  is 
again  compressed  within  the  coils  of  the  reservoir,  and  again  allowed  to 
expand  through  the  small  aperture  at  the  bottom.  Thus  after  a  few 
compressions  and  expansions  the  temperature  falls  more  and  more  until 
it  finally  sinks  to  the  point  where  liquefaction  begins.  After  this  stage  is 
reached  the  liquid  air  is  produced  continuously,  a  fresh  supply  of  air  being 
added  to  the  reservoir  from  time  to  time  to  take  the  place  of  that  which 
is  withdrawn  in  the  form  of  a  liquid.  The  boiling  point  of  liquid  air  is 
-191°  C. 

565  (Art.  252).     The  carbon  dioxide  in  the  breath  acts  with  the  calcium 
hydroxide  of  the  lime  water  in  accordance  with  the  following  chemical 
reaction:    C02  +  Ca  (OH)2  =  CaCOt  +H20.      It  is  assumed   that  when 
a  relatively  large  percentage  of  carbon  dioxide  is  present  in  the  air,  other 
and  poisonous  gases  are  also  present  in  harmful  quantities. 

566  (Art.  257).     An  air  thermometer,  as  shown  in  Fig.  201,  may  be  made 
from  Florence  flasks  by  fitting  into  the  necks  one-hole  rubber  stoppers 
containing  glass  tubes. 

667  (Art.  262).  The  steam  engine  is  a  machine  for  transforming  the 
potential  energy  of  coal  into  the  kinetic  energy  of  mechanical  motion. 
The  two  parts  of  the  complete  mechanism  are  the  boiler,  in  which  the 
energy  of  the  coal  is  transformed  into  the  energy  of  steam  under  pres- 
sure, and  the  engine  in  which  the  energy  of  the  steam  is  transformed 
into  mechanical  motion.  Most  of  the  heat  brought  to  the  engine 
by  the  steam  from  the  boiler  is  rejected  by  the  engine  in  the  exhaust. 
This  loss  of  heat  varies  from  70  per  cent  of  the  heat  of  the  steam 


SUPPLEMENT  375 

in  the  best  engines,  to  over  90  per  cent  in  the  poorer  types.  In  many 
manufacturing  establishments  the  heat  of  this  exhaust  steam  is  recovered 
by  using  it  for  heating  or  manufacturing  purposes.  In  some  modern 
engines  steam  is  superheated  previous  to  its  admission  to  the  engine. 
This  is  to  prevent  its  condensation  on  entering  the  expansion  chamber. 
By  means  of  the  use  of  superheated  steam  the  economy  of  a  simple  non- 
condensing  engine  may  be  made  nearly  equal  to  that  of  a  compound 
condensing  engine. 

Steam  engines  are  usually  classified  into  noncondensing  and  condensing 
engines,     (a)  A  noncondensing  engine  is  one  in  which  the  exhaust  steam 
passes  directly  from  the  cylinder  to  the  atmosphere.     In  this  case  the 
piston  always  works  against  a  back  pressure  of  one  atmosphere;  that  is, 
there  are  two  forces  acting  on  the  piston  when  it  is  in  motion.     One  is  the 
steam  tending  to  drive  it  in  one  direction,  and  the  other  is  atmospheric 
pressure  tending  to  drive  it  in  the  opposite  direc- 
tion.    It  is  clear,  therefore,   that  if  the  atmos- 
pheric pressure  could  be  removed  the  efficiency 
would  be  increased  to  the  extent  of  14.7  pounds 
per  square  inch,     (b)  The  condensing  engine  is 
one  in  which  the  exhaust  steam  passes  into  a 
cooling   chamber,   Fig.  531.     This   usually   con- 
sists  of  a  chamber   surrounded   by  water   and  FIG.  531 
into  which  a  spray  of  cold  water  is  admitted. 

When  the  steam  comes  in  contact  with  the  cold  spray  it  is  condensed, 
producing  a  partial  vacuum,  and  thus  reducing  the  back  pressure  on  the 
piston. 

Steam  engines  are  also  classified  as  simple  and  compound.  (a)  A 
simple  engine  is  one  in  which  the  steam  does  work  in  a  single  expansion, 
and  thus  passes  into  the  exhaust,  (b)  A  compound  engine  is  one  in  which 
the  steam  under  high  pressure  enters  one  cylinder,  does  work  upon  the 
piston,  then  enters  a  second  cylinder,  again  doing  work,  and  so  on.  When 
the  steam  exerts  its  pressure  upon  two  cylinders  in  succession,  the  engine 
is  called  a  double-expansion  engine;  when  it  acts  upon  three  cylinders, 
a  triple-expansion  engine,  etc.  In  many  of  our  ocean-going  vessels  engines 
are  used  of  the  quadruple-expansion  type. 

Engines  are  also  classified  as  reciprocating  and  turbine,  (a)  The 
reciprocating  engine  is  the  familiar  type,  in  which  a  piston  moves  back  and 
forth  in  the  cylinder,  (b)  In  the  steam  turbine,  Fig.  532,  steam  under 
high  pressure  is  driven  against  the  blades  of  a  wheel,  thus  causing  rotation. 
In  some  types  of  the  steam  turbine  the  steam  in  passing  through  the  rotat- 
ing system  strikes  successively  against  two  or  more  sets  of  blades  in  its 
passage  from  one  end  of  the  revolving  drum  to  the  other,  Fig.  533.  At 


376 


HIGH   SCHOOL   PHYSICS 


the  end  of  the  drum  where  the  steam  enters,  the  blades  are  smaller  than 
at  the  other  end,  the  steam  thus  in  moving  forward  expands,  doing  work 
at  the  expense  of  its  own  heat.  Steam  turbines  have  the  advantage  over 


FIG.  532.  —  Steam  Turbine 


FIG.  533 


reciprocating  engines  in  that  they  occupy  less  space  and  run  more  quietly. 
They  are  used  largely  on  steamships  and  in  running  electric  generators. 

668  (Art.  263).   The  Gas  Engine.     In  the  steam  engine  fuel  is  burned 
in  the  furnace,  generating  steam,  which  is  conveyed  from  the  boiler  to  the 


FIG.  534.  —  Diagram  of  Four-Cycle  Gas  Engine 


SUPPLEMENT 


377 


engine,  where  expansion  takes  place.  This  involves  at  every  step  a  waste 
of  energy.  In  the  gas  engine  the  entire  process  of  combustion  and  expan- 
sion takes  place  in  the  cylinder  itself.  A  mixture  of  air  and  gas,  or  of  air 
and  gasoline,  is  passed  into  the  cylinder  and  there  exploded.  This  pro- 
duces the  pressure  necessary  to  push  the  piston  forward.  The  cylinder 
is  supplied  with  two  valves,  an  inlet  and  an  outlet.  In  Fig.  534  there  is 
represented  the  four  steps  of  a  four-cycle,  single-cylinder  gas  engine,  (a) 
First,  the  flywheel  is  turned  by  hand,  or  other  device,  causing  the  piston  to 
move  down  and  thus  suck  in  a  mixture  of  air  and  gas  through  the  valve  i. 
(b)  As  the  flywheel  continues  its  rotation,  the  piston  moves  back,  com- 
pressing the  gas.  (c)  The  compressed  gas  now  explodes,  driving  the  piston 
forward,  (d)  On  the  back  stroke  of  the  piston  the  burnt  gases  are  ejected 
through  the  valve  o.  To  repeat,  the  four  steps  required  to  complete  the 
cycle  include  the  following:  Downward  stroke  of  piston  and  intake  of 
gas;  upward  stroke  of  piston  and  compression  of  gas;  explosion  of  gas, 
causing  downward  motion  of  piston;  upward  motion  of  piston  and  ejection 
of  gas.  The  explosion  of  gas  is  due  to  an  electric  spark,  which  is  timed  to 
occur  at  the  proper  moment.  Since  the  expanding  gas  acts  on  the  piston 
during  only  one  part  of  this  entire  operation,  it  is  necessary  in  gas  engines 
to  provide  a  heavy  flywheel,  the  momentum  of  which  is  sufficient  to  oper- 
ate the  piston  during  the  remaining  three  steps. 

The  gas  engine  just  described  is  called  a  four-cycle  engine;  that  is,  it 
requires  four  strokes  of  the  piston  to  complete  the  cycle.  An  engine  re- 
quiring two  strokes  to  the  cycle 
is  called  a  two-cycle  engine. 

The  efficiency  of  the  gas  en- 
gine, as  measured  by  the  num- 
ber of  B.T.U.  per  cubic  foot  of 
gas  consumed,  is  high,  25  per 
cent  or  greater.  It  must  be 
remembered  in  comparing  en- 
gine efficiencies  that  the  fuel 
used  by  the  gas  engine  is  more 
expensive  than  that  used  by  the 
steam  engine. 

669.  The  Toepler-Holtz  Ma- 
chine. The  Toepler-Holtz  ma- 
chine, Fig.  535,  is  provided  with 
two  glass  plates  of  which  A, 
Fig.  536,  is  stationary  and  B  is 
adjusted  so  as  to  rotate.  On  the  back  of  the  stationary  plate  there  are 
pasted  two  strips  of  tin  foil  C  and  D.  These  are  called  inductors.  On 


FIG.  535 
Toepler-Holtz  Static  Machine 


378 


HIGH  SCHOOL  PHYSICS 


the  rotating  disc  there  are  pasted  a  series  of  circular  carriers  a,  a',  a", 
a'",  made  of  tin  foil.  Each  carrier  has  in  its  center  a  metal  button  designed 
to  serve  as  a  contact.  Passing  from  one  inductor  to  the  other  there  is  a 
metal  rod  E.  The  conductors  which  approach  each  other  at  P  end  in 
metal  points  at  M  and  N,  and  communicate  also  with  two  small  Leyden 
jars.  Let  us  suppose  that  the  machine  is  in  action.  Inductors  A  and  B 
become  charged  to  a  certain  extent,  one  positively  and  the  other  nega- 
tively. Sometimes  this  charging  is  done  by  touching  one  of  the  inductors 
with  an  electrified  body;  usually,  however,  the  initial  rotation  of  the 
machine  is  sufficient  to  give  the  inductors  a  slight  initial  charge.  Now  as 
the  disc  rotates  in  the  direction  indicated,  let  us  consider  what  happens 


FIG.  536 

to  the  carrier  a.  As  it  passes  in  front  of  the  inductor  A,  it  becomes  elec- 
trified, the  —  charge  being  bound,  the  +  charge  free.  The  same  thing 
happens  on  carrier  a',  only  in  this  latter  case  the  +  is  bound  and  the  —  free. 
Now  when  the  two  carriers,  a  and  a',  pass  under  the  metal  brush  communi- 
cating with  the  metal  rod  E,  the  free  +  charge  on  one  neutralizes  the  free 
—  charge  on  the  other.  The  carrier  with  its  negative  charge  (a")  is  carried 
on  to  the  metal  brush  and  conductor  R.  It  is  here  transferred  to  the 
negatively  charged  inductor  D.  In  a  like  manner  the  carrier  with  its 
positive  charge  (a'")  is  carried  to  the  conductor  R',  and  thence  to  inductor 
C.  Thus  every  rotation  of  the  disc  tends  to  .charge  the  inductors  C  and 
D  to  a  high  potential,  C  with  a  +  charge  and  D  with  a  —  charge.  When 
these  inductors  become  highly  charged,  a  discharge  takes  place  between  the 
inductors  and  the  metal  points  M  and  N,  which  communicate  with  the 


SUPPLEMENT 


379 


Leyden  jars.  When  the  charge  on  the  Leyden  jars  becomes  sufficiently 
great  a  discharge-  takes  place  across  the  gap  at  P.  Thus  it  appears  that 
the  action  of  the  machine  is,  in  general,  similar  to  that  of  the  electrophorus. 

670.  The  Wimshurst  Machine.  The  essential  difference  between  the 
Wimshurst  and  the  Toepler-Holtz  machine  is  that  the  Wimshurst,  Fig.  537, 
has  two  plates  revolving  in  opposite  directions.  These  plates  carry  a 
large  number  of  tin  foil  strips 
which  act  alternately  as  induc- 
tors and  as  carriers.  This  does 
away  with  the  necessity  of  sep- 
arate inductors,  as  in  the  case  of 
the  Holtz  machine.  The  action 
of  the  machine  may  be  explained 
briefly  as  follows :  Only  the  slight- 
est difference  of  potential  is  nec- 
essary to  start  the  induction. 
Consider  that  the  sectors  near 
A  on  the  rear  plate  have  a 
slight  -f  charge.  This  will  in- 
duce a  —  charge  on  the  front 
rotating  plate,  which  communi- 
cates with  the  brush  on  the  rod 
CD.  The  free  +  charge  will  be 
repelled  along  CD  to  D.  The 

sector  at  A,  having  thus  been  -pIG  537 

charged  by  induction,  moves  on  Wimshurst  Static  Machine 

to   the  discharging  rods   at    E, 

charging  the  Leyden  jar  L.  In  a  similar  manner  the  sector  at  B,  having 
received  by  induction  a  +  charge,  moves  on  to  the  discharging  conduc- 
tor at  F,  charging  L'. 

671  (Art.  302).  Small  drops  of  moisture  or  particles  of  dust  on  elec- 
trical apparatus  designed  for  use  in  electrostatics  serve  as  discharging 
points.  In  order,  therefore,  to  perform  experiments  with  the  electroscope, 
electric  machine,  or  similar  instruments,  it  is  necessary  that  the  apparatus 
be  free  from  dust  and  that  the  experiments  be  performed  when  the  air 
is  dry. 

572  (Art.  313).  Polarization  is  that  which  occurs  in  the  cell  tending 
to  reduce  its  E.M.F.  Polarization  may  be  due  to  (a)  a  change  in  con- 
centration of  the  electrolyte  or  (b)  to  a  collection  of  gas,  as  hydrogen  for 
example,  on  the  positive  electrode.  The  reason  that  hydrogen  reduces 
the  E.M.F.  of  the  cell  is  mainly  due  to  the  fact  that  this  element  (H)  acts 
toward  zinc  like  a  metal,  the  E.M.F.  of  the  combination  H-Zn  opposing 


380  HIGH  SCHOOL  PHYSICS 

the  E.M.F.  of  the  Zn-Cu  electrodes,  and  thus  diminishing  the  electro- 
motive force  of  the  cell. 

673  (Art.  317).  By  "closed  circuit  work"  we  mean  work  similar  to 
that  in  connection  with  the  telegraph  system.  When  the  operator  is 
through  sending  his  message  he  closes  his  switch  or  key,  and  the  current 
flows  around  the  circuit  until  the  next  message  is  sent;  hence  the  name 
closed  circuit.  Of  course  every  time  the  key  is  pressed  down  the  circuit 
is  closed  momentarily.  A  closed  circuit  then,  as  used  in  this  sense,  means 
a  circuit  that  is  closed  when  not  in  use.  An  open  circuit,  on  the  other 
hand,  is  one  which  is  open  when  not  in  use,  as  is  illustrated  by  the  ordinary 
doorbell  circuit. 

674.  The  Lead  Storage  Battery.  The  complete  chemical  reactions 
which  occur  in  the  charge  and  discharge  of  storage  batteries  are  not  defi- 
nitely known.  In  the  case  of  the  lead  cell,  however,  we  may  represent 
the  condition  of  the  plates  of  the  cell  when  charged  as  follows:  Positive 
plate  =  PbO2;  negative  plate  =  Pb.  On  discharge  there  is  formed  on 
both  plates  lead  sulphate,  PbSO4. 

Lead  storage  cells  have  relatively  high  E.M.F.,  2.1  volts  when  charged. 
They  have  an  exceedingly  low  internal  resistance,  less  than  0.1  ohm. 
If  a  storage  cell,  therefore,  be  short  circuited,  the  current  through  the  cell 
is  excessively  high.  The  lead  storage  battery  is  a  very  efficient  and  useful 
piece  of  apparatus.  It  is  also  an  expensive  piece  of  apparatus,  and  it  is, 
therefore,  important  to  observe  the  following  cautions  with  reference  to 
these  cells: 

(a)  The  lead  cell  should  never  be  short  circuited.     A  cell,  for  example, 
in  which  the  E.M.F.  is  2  volts  and  the  internal  resistance  0.02  of  an  ohm 
would  furnish  on  short  circuit  a  current  of  100  amperes,  which  would  be 
ruinous  to  the  cell. 

(b)  The  cell  should  not  be  overcharged.     Overcharging  causes  over- 
heating, which  causes  the  plates  to  bend  or  "buckle/'  thus  crowding  the 
lead  peroxide  out  of  the  "grids"  or  holes  in  the  plate. 

(c)  The  cell  should  not  be  over-discharged,  that  is,  discharged  below  an 
E.M.F.  of  1.8  volts.     Over-discharge  causes  an  excessive  formation  of  lead 
sulphate  on  the  plates,  which  permanently  impairs  their  efficiency. 

(d)  Only  distilled  water  should  be  used  in  making  up  the  sulphuric 
acid  solution  used  as  the  electrolyte.     Impurities  in  the  electrolyte  are 
fatal  to  the  life  of  the  cell. 

575.  The  Edison  Storage  Battery.  The  Edison  storage  cell  has  re- 
cently been  put  upon  the  market.  Less  is  known  of  the  chemical  reactions 
occurring  in  this  cell  than  in  that  of  the  lead  cell.  The  positive  electrode 
of  the  Edison  cell  consists  of  a  nickel  plate,  the  negative  electrode  of  an  iron 
plate.  The  electrolyte  is  a  21  per  cent  solution  of  potassium  hydroxide, 


SUPPLEMENT 


381 


KOH,  in  pure  distilled  water.  On  charge  the  nickel  plate  is  oxidized  to 
NiO2.  On  discharge  the  nickel  is  reduced  to  Ni2Os  and  the  iron  is  oxidized 
to  FeO. 

The  E.M.F.  of  an  Edison  cell  is  1.2  volts.  Its  capacity  is  16.8  watt 
hours  per  pound;  that  of  a  lead  cell,  8.5  watt  hours  per  pound.  It  is  said 
that  an  Edison  cell  is  not  injured  by  short  circuiting.  The  "life"  of  these 
cells  under  commercial  conditions  is  as  yet  undetermined. 

576  (Art.  348).     Manganin  is  a  metal  consisting  of  an  alloy  of  12  per 
cent  manganese,  84  per  cent  copper,  and  4  per  cent  nickel.     The  reason  for 
its  use  in  resistance  coils  lies  in  the  fact  that  its  change  of  resistance  with 
change  of  temperature  is  almost  zero. 

577  (Art.  362).     We  sometimes  connect  the  cells  of  a  storage  battery  in 
parallel,  not  for  the  purpose  of  reducing  the  internal  resistance,  but  in  order 
to  permit  of  a  larger  current  being  drawn  from  it  with  safety  to  the  cells. 
This  is  due  to  the  fact  that  the  current  capacity  of  a  storage  cell  depends 
upon  the  area  of  the  plate.     Therefore,  the  greater  the  plate  area  (secured 
by  connecting  in  parallel)  the  greater  the  current  capacity  of  the  system. 

578  (Art.  368).     The  carbon  in  an  arc  lamp  may  be  adjusted  by  three 
methods:    (a)  By  hand;    (b)  by  a  clock-work  device;    (c)  by  a  system  of 
electromagnets. 

In  the  arc  lamp  used  in  the  ordinary  laboratory  lantern  the  adjustment 
of  the  carbons  is  made  by  hand,  by  means  of  a  set  of  thumb  screws.  In 
the  commercial  arc  light  a  set  of  electromagnets  are  operated  in  such  a 
way  that  when  the  arc  is  broken  and  the  current  dies  to  zero,  the  armature 
•of  the  electromagnet  falls,  allowing  the  carbon  tips  to  touch.  As  soon 
as  the  circuit  is  thus  completed  the  electromagnet  attracts  the  armature, 
thus  drawing  the  carbons  apart  and  forming  the  arc. 

579  (Art.  396).     A  diagram  of  a  more  complete  line  and  local  telegraph 
system  is  shown  in  Fig.  538.     Two  stations  are  represented,  one  at  H  and 


Diagram  of  Telegraph  System 


382  HIGH  SCHOOL  PHYSICS 

one  at  P.  When  the  resistance  of  the  line  is  very  high,  the  current  is 
sometimes  too  weak  to  operate  the  sounder.  To  overcome  this  difficulty 
a  local  circuit  consisting  of  the  sounder  and  local  battery  is  connected  to 
the  main  circuit  by  means  of  a  relay,  Fig.  539.  The  relay  resembles  the 


FIG.  539.  —  Telegraph  Relay 

sounder  in  form.  It  consists  of  an  electromagnet  of  many  turns  of  fine 
wire  and  is  designed  to  be  operated  by  very  weak  currents.  As  the  arma- 
ture of  the  relay  moves  back  and  forth  in  response  to  the  line  current,  it 
opens  and  closes  the  local  switch,  thus  causing  the  local  battery  to  operate 
the  sounder. 

580  (Art.  409).  Wireless  Telegraphy.  When  the  spark  passes  between 
the  knobs  of  an  induction  coil  or  an  electric  machine,  a  violent  rush  of 
electricity  occurs,  which  may  be  accompanied  by  electrical  oscillations  in 
any  conductors  connected  with  them.  This  electric  surging  gives  rise  to 
an  electric  disturbance  which  spreads  out  through  space.  The  existence 
of  such  a  disturbance  was  demonstrated  by  the  brilliant  experiments  of 
Hertz.  Now  when  this  electric  disturbance  reaches  a  distant  conductor  it 
causes  a  somewhat  corresponding  disturbance  in  the  conductor. 

In  1890  Branly  and  Lodge  prepared  a  delicate  detector  for  these  electric 
disturbances,  now  known  as  Hertz  waves.  This  detector  is  called  a  coherer, 


FIG.  540.  —  Coherer 

Fig.  540.  It  consists  of  a  glass  tube  loosely  packed  with  metal  filings. 
When  the  coherer  is  placed  in  an  ordinary  battery  circuit  it  offers  such  a 
high  resistance  that  scarcely  any  current  will  pass  through  it.  It  was 
discovered,  however,  that  if  an  electric  spark  be  produced  in  a  near-by  coil 
the  filings  in  the  tube  at  once  conduct  readily  and  continue  to  act  as  a  good 
conductor  until  the  tube  is  disturbed  by  tapping.  The  Italian  physicist, 


SUPPLEMENT 


383 


Marconi,  seized  upon  this  discovery  and  after  much  experimentation  devised 
an  apparatus  which  would  respond  to  the  Hertz  waves  over  a  distance  of 
hundreds  of  miles. 

In  the  modern  commercial  wireless  telegraph  there  are  several  different 
types  of  detectors  in  use.  They  may  be  classified  as  follows:  (a)  Coherers; 
(b)  magnetic  detectors;  (c)  thermal  detectors;  (d)  crystal  detectors; 
(e)  electrolytic  detectors,  and  (f)  vacuum  detectors. 

The  coherer  has  practically  gone  out  of  use  in  commercial  work.  Some 
form  of  the  crystal  rectifier  is  now  generally  employed  as  a  detector.  It 
would  be  difficult  at  this  time,  however,  to  predict  just  which  one  of  the 
various  types  of  detectors  will  ultimately  prove  to  be  the  most  satisfactory. 


-E 

FIG.  541.  — Wireless  Telegraph 
Receiving  Station 


FIG.  542.  — Wireless  Telegraph 
Sending  Station 


In  Fig.  541  there  is  shown  a  receiving  system  in  which  a  crystal  rectifier 
R  is  used.  Certain  crystals,  especially  those  of  carborundum,  have  the 
property  of  allowing  the  current  to  pass  through  them  in  one  direction 
only.  The  resistance  of  such  crystals  is  also  modified  by  oscillatory  dis- 
charges. When  electric  oscillations  are  received  by  the  antennae  A,  or 
receiving  wire,  the  resistance  at  the  contact  point  of  the  crystal  appears  to 
be  changed,  allowing  a  slight  current  from  the  battery  to  flow  through  the 
telephone,  and  thus  giving  rise  to  a  crackling  sound. 


384 


HIGH  SCHOOL  PHYSICS 


A  sending  station  is  represented  in  Fig.  542.  The  sending  antennae 
are  represented  by  A.  H  is  a  helix  which  gives  rise  to  self-induction,  the 
adjustment  of  which,  together  with  that  of  the  capacity  of  the  condenser 
C,  enables  the  instrument  to  be  tuned  for  long-distance  transmission.  /  is 
an  induction  coil  which  is  operated  by  means  of  the  key  K.  S  represents 
the  spark-gap.  When  the  key  is  operated,  a  series  of  brilliant  discharges 
occur  at  *S,  giving  rise  to  a  series  of  oscillatory  impulses  which  are  com- 
municated to  the  surrounding  space.  These  electrical  impulses  are  caught 
by  the  receiving  antennae  and  the  message  read  by  means  of  the  telephone. 

581  (Art.  454).     It  is  quite  common  to  speak  of  the  tension  on  a  string 
when  referring  to  the  stretching  force  applied  to  it.     The  word  tension  when 
used  in  a  strictly  scientific  sense  means  force  per  unit  of  area.     The  term 
pressure  represents  a  push  per  unit  of  area,  and  tension  a  pull  per  unit  of 
area.     In  this  text  the  word  stretching  force  is  used  instead  of  the  word 
tension. 

582  (Art.  460).    Conditions  in  a  Sounding  Pipe.     In  order  to  get  a  clear 
understanding  of  what  takes  place  in  a  pipe  when  it  emits  a  given  note, 

__.„  let  us  consider  what  happens  in  an  open  pipe,  Fig.  543,  which 
is  sounding  its  fundamental  in  response  to  the  vibrations  of 
a  tuning  fork.  It  is  necessary  to  note  that  when  the  fork 
moves  downward,  a  condensation  is  thrown  downward  and 
a  rarefaction  upward,  and  when  the  fork  moves  upward 
a  condensation  is  thrown  upward  and  a  rarefaction  down- 
ward. 

Now  when  the  fork  moves  down,  the  condensation 
runs  down  the  pipe  and  on  reaching  the  end  passes  out, 
giving  rise  to  a  rarefaction  which  starts  back  toward  the  fork. 
At  this  same  instant  the  fork  starts  on  its  return  path  up- 
ward, thus  sending  a  rarefaction  into  the  pipe.  These  two 
.  rarefactions  meet  and  pass  each  other,  at  the  middle  point  N. 
The  rarefaction  which  is  moving  down  the  pipe  reaches 
the  end  and  passes  out,  giving  rise  to  a  condensation  which 
starts  upward.  At  the  same  instant  the  fork  ^  moves 
downward,  sending  a  condensation  into  the  pipe.  These 
two  condensations  meet  and  pass  at  the  middle,  thus  forming,  for  an  in- 
stant, a  double  condensation.  At  the  instant  of  the  formation  of  a  double 
condensation  the  pressure  is  greater  than  an  atmosphere,  and  at  the  in- 
stant of  the  formation  of  a  double  rarefaction  it  is  less  than  an  atmos- 
phere. This  point  of  the  meeting  of  condensation  with  condensation,  and 
rarefaction  with  rarefaction,  is  called  a  node. 

583.  Nodes  and  Antinodes  in  Pipes.  A  node  N  in  a  pipe  is  the  point  of 
least  motion  and  greatest  change  of  pressure.  In  this  latter  respect  a 


FIG.  543 


SUPPLEMENT 


385 


node  in  a  pipe  differs  in  a  very  marked  way  from  a  node  in  a  string.  As 
we  have  seen,  the  change  of  pressure  at  the  node  is  due  to  the  appearance 
of,  first,  a  double  condensation,  and  then  a  double  rarefaction  at  that 
point,  giving  rise  to  a  maximum  change  of  pressure.  This  can  be  shown 
by  making  an  opening  in  the  pipe  at  N  and  placing  over  the  same  a  thin 
membrane.  When  the  double  condensation  occurs  at  N  the  membrane  will 
be  forced  outward;  when  the  double  rarefaction  occurs  the  membrane 
will  be  forced  inward.  Thus  the  passage  of  the  condensations  and  rare- 
factions along  the  pipes  will  give  rise  to  a  fluttering  of  the  membrane  at 
the  node. 

To  summarize  then,  a  node  in  a  pipe  is  the  point  of  least  motion  and 
greatest  change  of  pressure;  an  antinode  is  the  point  of  greatest  motion 
and  least  change  of  pressure. 

684.  Nodes  in  Open  Pipes.  Fig.  544  shows  the  postion  of  the  nodes 
in  the  production  of  the  fundamental  and  the  first  two  overtones  of  an 
open  pipe.  In  pipe  A,  sounding  its  fundamental, 
the  node  is  at  the  center  and  the  length  of  the 
pipe  is  one-half  the  wave  length  of  the  sound 

emitted.      In    pipe     B 

there    are    two    nodes, 

hence  the  pipe  is  sound- 
ing  its    first    overtone; 

that  is,  it  gives  a  pitch 

one  octave  higher  than 

A.     In  pipe  C  there  are 

three  nodes;  the  pipe  is 

sounding    its    second 

overtone. 

In  open  pipes  there  is 

always  an  antinode  at 

each    end    and    one    or 

more  nodes  within  the 

pipe.     Also,  open  pipes 

are  capable  of  sounding 

in     addition     to     their 

fundamental  tone  their 

first,  second,  third,  fourth,  fifth,  etc.,  overtones. 
585.   Nodes  in  Closed  Pipes.     Pipe  Z>,  Fig. 

545,  represents  a  closed  pipe  sounding  its  funda- 
mental; E  represents  the  same  pipe  giving  its  first 
overtone,  the  vibration  rate  of  which  is  three  times  that  of  the  funda- 
mental; F  is  sounding  the  next  overtone,  which  is  five  times  the  vibration 


\    i 

\    i 

\        ' 

\  i 

t       f 

\  i 

i      / 

\  i 

\     / 

-  -X  — 

\     > 

\   / 

/\ 

\  ' 

'      \ 

1 

y 

'•        \ 

1 

"?v 

' 

/    \ 

1 

/      \ 

1        1 

/      \ 

,            / 

1      1 

1       \ 

\     / 

\      / 

1     1 

1            1 

\  / 

1     1 

1    1 

•-  4— 

1   ; 

/  \ 
*     \ 

'       \ 

1  i 

'         \ 

i  i 

1 

i  / 

\        ,' 

1  1 

y 

y 

\/ 

V 

v 

w 

D           E           F 

FIG.  545 

\        / 

\      i 

\      / 

\    / 

\     , 

\  / 

\    / 

"~/*T 

\  / 

\/ 

/    \ 

1 

--X— 

/     \ 

1 

A 

/       \ 

\        1 

/  \ 

\       1 

'    \ 

\     I 

/     \ 

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i      i 

i      \ 

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\    1 

\    / 

\l 

\  / 
\/ 

—  x  — 

—  A— 

;\ 

1 

/  \ 

,  \ 

i      , 

/       \ 

;    \ 
'    i 

\      , 
\     * 

/        \ 

I     \ 
\ 

\j 

!      \ 

\  / 

^        I 

\ 

—  Y  — 

\      / 

/  \ 

\    / 

/  \ 

\  / 

/    \ 

--\-~ 

/     \ 

i  \ 

/      \ 

1    \ 

\ 

1      \ 

i        \ 

A 

B 

C 

FIG.  544 

386  HIGH  SCHOOL  PHYSICS 

rate  of  D.     Closed  pipes  are  capable  of  giving  only  the  first,  third,  fifth, 
etc.,  overtones. 

586.  The  old  standard  of  candle   power  was  the  light  furnished  by  a 
sperm  candle  burning  at  the  rate  of  120  grains  per  hour.     The  modern 
standard  candle  unit  is  the  light  equal  in  intensity  to  1.136  hefner  units. 
A  hefner  unit  is  the  intensity  of  a  horizontal  beam  of  light  from  a  Hefner 
lamp,  so  named  in  honor  of  its  inventer.     The  Hefner  lamp  burns  pure 
amyl  acetate,  under  definitely  prescribed  conditions  of  wick  and  flame 
adjustment. 

587.  Formula  for  Images  Formed  in  Spherical  Mirrors.     The  relation 
between  the  position  of  the  image  and  the  object  with  reference  to  spherical 
mirrors  is  written 

1  +1=2 

p  p'          T 

in  which  p  is  the  distance  of  the  object  from  the  vertex  of  the  mirror,  p'  the 
distance  of  the  image  from  the  mirror,  and  r  the  radius  of  the  mirror. 

Example.  A  lighted  candle  is  placed  at  a  distance -of  20  inches  from 
the  vertex  of  a  spherical  mirror,  the  radius  of  curvature  r  of  which  is  8 
inches.  How  far  from  the  mirror  is  the  image? 

112  112 

Solution :   —  +  — -  =  -;  therefore  — -  +  — -,  =  5  5  hence  p'  =  5  inches, 
p      p         r  2\j       p         o 

588.  Formulae  for  Images  Formed  by  Lenses.     The  relation  between 
the  distance  of  an  object  from  a  lens  and  the  distance  of  the  image  may  be 
expressed  by  the  following  equations: 

(a)  For  the  convex  lens  when  the  object  is  at  a  distance  from  the  lens 
greater  than  the  focal  length: 

ui-i 

9      .P       f 

(b)  For  the  convex  lens  when  the  object  lies  between  the  principal  focus 
and  the  lens: 

1  _  1  =  _  1 

9       P  f 

(c)  For  the  concave  lens: 

1  _   1    =  1 

2  P   ~  f 

Example.  An  object  is  placed  30  centimeters  from  a  convex  lens,  the 
focal  length  of  which  is  10  centimeters.  Find  the  position  of  the  image. 

Solution :  -  +  -  =  -;  therefore,  -  +  ^  =  TT:  ',  hence  q  =  15  centimeters. 


SUPPLEMENT 


387 


689  (Art.  498).  The  index  of  refraction  may  also  be  denned,  and 
indeed  is  commonly  defined,  as  the  ratio  of  the  sine  of  the  angle  of  incidence 
to  the  sine  of  the  angle  of  refraction.  This  assumes  of  course  that  the 
student  knows  the  meaning  of  the  terms  sine  and  cosine  as  defined  in 
trigonometry. 

590.  The  Compound  Microscope.  This  is  an  instrument  which  is 
designed  to  give  a  highly  magnified  image  of  very  small  objects.  It  con- 
sists of  two  lenses  or  sets  of  lenses,  E  called  the  eyepiece  and  0  called  the 
objective,  Fig.  546.  The  object  to  be  examined,  AB,  is  placed  beyond  the 


principal  focus  F  of  the  objective.  This  gives  a  real,  inverted  image  a&, 
which  lies  between  the  principal  focus  of  the  eyepiece  and  the  lens.  This 
image  ab  gives  through  E  a  virtual  magnified  image  A'B',  which  is  observed 
by  the  eye  at  DC. 

591.  The  Telescope.  In  the  case  of  the  telescope  the  arrangement 
of  the  lenses  is  not  very  much  different  from  that  of  the  compound  micro- 
scope. The  main  difference  is  in  the  relative  sizes  for  the  objective  lens. 
In  the  telescope,  which  is  designed  to  view  distant  objects,  the  objective 
lens  is  of  large  aperture  and  longer  focal  length.  The  reason  for  making 
the  objective  large  is  for  the  purpose  of  collecting  within  the  instrument 
as  much  light  as  possible,  so  as  to  permit  of  large  magnification  without 
too  great  loss  in  brightness. 


FIG.  547 

The  relative  position  of  the  lenses  and  the  formation  of  the  virtual 
image  A  'E'  is  shown  in  Fig.  547. 

592.   The  Binocular  Glass.     The  binocular  field  glass,   Fig.   548,   is 


388 


HIGH   SCHOOL  PHYSICS 


short,  compact,  and  has  a  system  of  lenses  for  each  eye.  The  arrangement 
of  the  objective  and  the  eyepiece  are  practically  the  same  as  in  the  astro- 
nomical telescope,  but  the  necessary  distance  between  them  is  obtained 
by  having  the  light  travel  the  length  of  the  tube 
three  times  in  passing  from  the  objective  to  the 
eyepiece.  This  is  accomplished  by  reflection  by 
means  of  a  system  of  prisms  within  the  tube  of 
the  instrument.  This  reflection  of  the  light 
within  the  instrument  not  only  shortens  the 
tube,  but  also  causes  the  image  to  appear  erect. 
593.  The  Projection  Lantern.  The  electric 
arc  is  almost  universally  used  as  the  source  of 
light  for  projection  purposes,  although  other 
sources  may  be  employed,  such  as  the  acetylene 
light.  The  carbons  forming  the  arc  are  ad- 
justed to  touch  at  right  angles,  Fig.  549.  The 
upper  carbon  is  positive  in  the  case  of  a  direct  current,  thus  throwing  the 
brilliant  light  from  the  crater  directly  upon  the  screen. 

The  projection  device  consists  essentially  of  two  optical  systems,  one 
called  the  condenser,  lens  C,  the  function  of  which  is  to  condense  the 


FIG.  548 
Binocular  Field  Glass 


FIG.  549 


divergent  rays  from  the  arc  upon  the  slide  S',  the  other  is  the  objective 
lens  0,  the  function  of  which  is  to  focus  the  light  upon  the  screen.  The 
image  is  real  and  inverted. 

694  (Art.  621).  The  Rainbow.  In  Fig.  550  we  have  given  a  more  or 
less  ideal  sketch  illustrating  the  relation  of  the  primary  to  the  secondary 
bow  with  reference  to  the  number  of  reflections  and  refractions  in  each. 
The  margin  of  each  bow  is  selected  for  illustration.  In  order  to  see  both 
bows,  the  eye  E  must  be  in  such  a  position  with  respect  to  the  sun  S  that 
the  light  refracted  and  dispersed  by  the  drops  will  make  a  definite  angle 
with  the  line  of  direction  of  the  sun's  rays.  This  angle  depends  upon  the 


SUPPLEMENT  389 

index  of  refraction  of  the  drop  and  the  color  seen  by  the  eye.  This  angle 
varies  from  color  to  color  since  the  index  of  refraction  of  the  different 
colors  of  the  spectrum  vary.  The  angle  REC  for  red  of  the  primary  bow 
is  42°,  that  of  violet,  VEC,  40°;  for  the  secondary  bow  the  angles  are,  for 
violet  54°,  for  red  51°.  The  reason  that  the  rainbow  is  circular,  then,  is 
that  the  color  from  only  those  drops  which  make  a  definite  angle  with  EC 
are  seen  by  the  eye.  In  other  words,  the  eye  is  at  the  vertex  of  a  cone,  a 
portion  of  the  base  of  which  is  a  circle  forming  the  rainbow. 


C 

FIG.  550.  —  Diagram  showing  Formation  of  Primary  and 
Secondary  Rainbows 

It  will  be  observed  that  light  forming  a  primary  bow  suffers  two  refrac- 
tions and  one  internal  reflection;  the  secondary  bow,  two  refractions  and 
two  reflections.  Now  since  some  light  is  lost  at  each  reflecting  surface, 
it  is  easy  to  understand  why  the  primary  bow  is  the  brighter  of  the  two. 

Theoretically,  several  secondary  bows  are  possible,  and  with  very 
bright  sunlight  three  are  occasionally  seen.  As  a  rule,  however,  only  the 
primary  and  a  portion  of  the  secondary  are  visible.  It  is  well  to  note  in 
this  connection  that  the  phenomenon  of  the  rainbow  is  much  more  complex 
than  this  simple  discussion  might  imply.  Sometimes  "spurious"  bows  are 
seen  on  the  inner  edge  of  the  primary.  These  have  formed  the  subject  of 


390  HIGH  SCHOOL  PHYSICS 

much  recent  investigation,  which   leads  to  the  supposition  that  they  are 
due  to  interference  phenomena. 

595.  The  Electron  Theory.     Investigations  of  the  nature  of  the  cathode 
rays  have  led  to  what  is  now  known  as  the  electron  theory  of  matter.     The 
cathode  rays  are  made  up  of  tiny  particles  called  electrons.   These  elec- 
trons, or  corpuscles  as  they  are  sometimes  called,  are  negative  charges  of 
electricity.     Whether  they  have  mass  in  the  sense  that  ponderable  matter 
has  is  not  definitely  known.      It  has  been  calculated  that  the  apparent 
mass  of  an  electron  should  increase  with  its  velocity,  and  this  surprising 
result  has  been  verified  experimentally.     In  other  words,  the  apparent 
mass  of  the  electron  may,  in  a  sense,  be  accounted  for  by  its  velocity.     It 
has  been  found  also  that  the  electrons  of  which  the  cathode  rays  are  com- 
posed are  identical,  regardless  of  the  source  from  which  they  come.     This 
suggests  that  the  electrons  are  the  common  constituents  of  all  atoms. 
Indeed,  it  has  been  suggested,  that  the  atom  may  be  nothing  more  than  a 
collection  of  electrons,  and  that  the  nature  of  the  individual  atom  may  be 
determined  by  the  number  of  electrons  which  it  contains  and  the  character 
of  their  motions. 

While  much  that  has  been  written  regarding  electrons  is  pure  specula- 
tion, yet  there  is  a  scientific  basis  of  fact  for  the  statement  that  in  the  very 
near  future  not  only  will  much  of  the  phenomena  of  electrical  discharge 
and  conduction  be  explained  in  terms  of  this  theory,  but  also  that  it  will 
have  a  very  general  application  to  the  phenomena  of  light  and  heat  as  well. 

596.  Radio-activity.     The  discovery  of  the  X-ray  by  Roentgen  was 
followed  by  great  activity  in  the  researches  into  the  nature  of  electric 
discharge.     In  1896  Becquerel,  a  French  chemist,  discovered  that  the 
element  uranium  and  all  its  compounds  emit  rays  which  are  capable  of 
penetrating  thin  plates  of  metal  and  other  substances  opaque  to  ordinary 
light.     A  few  years  later  M.  and  Mme.  Curie  extracted  from  pitch-blend 
a  substance  which  they  called  radium,  and  which  is  many  thousand  times 
more  radio-active  than  uranium.     Radium  possesses  the  startling  prop- 
erty of  maintaining  its  temperature  several  degrees  above  that  of  the 
air  and  of  radiating  heat  energy  without  any  apparent  supply  being  im- 
parted to  it.     The  rays  emitted  by  radium  are  of  three  kinds:    (a)  o-rays 
(alpha  rays),  which  are  positively  charged  and  have  a  very  low  power  of 
penetrating  solids;  (b)  /8-rays  (beta  rays),  which  are  negatively  charged 
and  are  more  penetrating  than  the  o-rays;  (c)  y-rays  (gamma  rays),  which 
have  some  of  the  properties  of  X-rays,  and  which  have  great  penetrating 
power. 

Further  investigations  add  to  the  conclusion  that  uranium  when  left 
to  itself  undergoes  a  change  which  consists  in  the  formation  of  other 
substances.  One  of  the  products  of  the  disintegration  of  uranium  appears 


SUPPLEMENT  391 

to  be  radium,  which  in  turn  disintegrates  into  still  other  substances.  A 
complete  series  of  the  products  of  radium,  which  is  itself  probably  a  dis- 
integration product  of  uranium,  has  been  worked  out  by  the  English 
scientist  Rutherford. 

The  facts  upon  which  the  theory  of  radio-activity  is  based  seem  to 
lead  to  the  conclusion  that  in  the  disintegration  of  uranium  to  radium,  and 
from  radium  to  other  elements,  we  have  a  transformation  of  one  element 
into  another  element.  We  can,  therefore,  no  longer  use  the  old  definition 
of  an  element;  namely,  that  an  element  is  a  substance  that  cannot  be 
broken  up  into  another  substance. 

597  (Art.  285).  Theories  of  Electrification.  There  are  several  theories 
relative  to  the  nature  and  cause  of  the  phenomenon  known  as  electrifica- 
tion. The  two-fluid  theory  assumes  the  existence  of  two  kinds  of  electricity, 
called  positive  and  negative.  It  has  been  generally  agreed  to  call  the 
electric  charge  found  on  glass  rubbed  with  silk  positive,  and  that  found  on 
sealing  wax  or  hard  rubber  when  rubbed  with  flannel  or  cat's  fur  negative. 
This  theory  permits  of  an  easy  and  simple  description  of  the  fundamental 
phenomena  of  static  electricity,  and  lends  itself  readily  to  the  solution  of 
elementary  problems. 

The  one-fluid  theory  was  first  proposed  by  Benjamin  Franklin.  Accord- 
ing to  this  view  a  body  is  positively  charged  when  it  has  more  than  its 
share  of  the  electric  fluid,  and  negatively  charged  when  it  has  less  than 
its  normal  share. 

The  electron  theory  (Art.  595)  assumes  that  electrons  are  elementary 
negative  charges  of  electricity,  and  that  an  electric  current  is  mainly  due 
to  a  transfer  of  electrons  through  a  conductor.  The  electron  theory,  com- 
bined with  the  ether-strain  theory  of  Faraday  and  Maxwell,  conceives  of 
an  electrified  body  as  having  tubes  of  induction  radiating  out  from  it  in 
all  directions.  These  tubes  of  induction  are  supposed  to  extend  from  a 
positively  charged  body  to  a  negatively  charged  one.  The  phenomena 
of  attraction  may  thus  be  explained,  in  a  manner  somewhat  similar  to 
that  given  in  magnetism,  by  assuming  that  these  tubes  always  tend  to 
shorten,  and  also  that  they  exert  a  lateral  pressure  upon  each  other. 

None  of  the  theories  offered  in  explanation  of  electrical  phenomena 
are  entirely  satisfactory.  They  all,  no  doubt,  possess  some  elements  of 
truth.  The  electron  theory,  when  thoroughly  worked  out,  will  undoubt- 
edly get  us  well  along  the  road  to  a  more  complete  understanding  of  many 
electrical  manifestations  which  are  now  inexplicable. 

598  (Arts.  255,  469).  Radiation.  —  The  spread  of  a  disturbance  radially 
from  a  source  is  called  radiation.  The  fundamental  point  to  be  kept  in 
mind  in  connection  with  a  study  of  radiation  is  that  there  is  a  transmis- 
sion of  energy  outward  from  a  center  through  some  sort  of  a  medium. 


392  HIGH  SCHOOL  PHYSICS 

While  in  a  general  sense  the  transmission  of  sound  waves  through  air  is  a 
phenomenon  of  radiation,  yet  the  term  is  now  usually  restricted  to  ether 
radiations.  Radiant  energy  may  give  rise  to  electrical,  optical,  chemical, 
or  thermal  phenomena. 

The  question  at  once  arises  as  to  the  nature  of  the  medium  by  means 
of  which  this  radiant  energy  is  transmitted.  This  medium  is  called  the 
ether.  We  do  not  know  positively  that  such  a  medium  really  exists;  we 
only  assume  that  it  exists.  We  cannot,  then,  speak  with  any  degree  of  defi- 
niteness  of  its  properties;  indeed  the  properties  of  the  ether  are  as  much 
a  question  of  dispute  today  as  they  were  in  the  days  of  Newton.  While, 
then,  it  is  convenient  and  even  necessary  to  assume  that  there  is  some 
such  medium  by  means  of  which  radiant  energy  may  be  transmitted,  we 
should  nevertheless  be  very  careful  not  to  allow  our  assumptions  to  come 
to  be  regarded  as  facts.  In  this  text,  therefore,  we  speak  of  the  ether 
merely  as  a  medium  capable  of  transmitting  energy,  without  specifying 
whether  this  transmission  is  due  to  the  elastic  properties  of  the  medium, 
to  strain  tubes,  or  to  any  other  specific  means  whatsoever. 

It  may  not  be  out  of  place  here  to  mention  that  there  are  today  a  number 
of  theories  relative  to  the  ether  which  attempt  to  explain  all  the  phenomena 
of  the  transmission  of  radiant  energy.  One  of  the  most  modern  is  that 
known  as  the  electron  theory  of  radiation.  This  theory,  briefly  stated, 
assumes  that  the  disturbances  propagated  through  the  medium,  as  light 
from  the  sun  for  example,  are  due  to  electric  disturbances  in  the  source. 
Atoms  may  be  considered  as  made  up,  in  part  at  least,  of  electrons.  It  is 
assumed  that  the  vibrations  of  the  electrons  of  the  source  of  radiant  energy 
produce  electromagnetic  disturbances  in  the  ether;  they  thus  serve  as  centers 
of  electromagnetic  radiation.  This  theory,  in  short,  assigns  as  the  source 
of  radiant  energy,  as  light  for  example,  electric  disturbances  in  the  body, 
rather  than  elastic  vibrations  of  the  atoms  or  molecules  of  the  body. 


SUPPLEMENT 


393 


599.                                      TAB 

DENS] 

Air,  at  0°  C.  and  76  cm. 
pressure      ....       0.00129 
Alcohol                                    °  sn 

LES 

TIES 

Iron,  cast 
Iron,  wrought 
Ivory                     .      . 

.       7.40 

7.86 
1.82 

Aluminum 
Antimony 

.      .       2.67 
.      .       6.72 

Lead                           . 

11.30 

Magnesium    . 
Marble            .      .      . 

1.75 
2.72 

096 

Bismuth 

982 

Mercury,  at  0°  C.     . 
Milk    

.      13.596 
1.03 

Brass 

85 

Charcoal 

1  60 

Nickel                   .      . 

8.9 

Coal          .      .      . 
Copper 

1.3  to     1.80 
.      .       8.9 

Olive  oil 

0.92 

Paraffin     .... 
Platinum        .      .     . 
Silver 

.       0.90 
.     21.50 
10.56 

Cork          .      .      . 

.      .       0.24 

Diamond. 

3  53 

Ether 

074 

Steel    

7.82 

German  silver 
Glass,  crown  . 
Glass,  flint 
Glycerine  . 
Gold    .... 

.      .       8.43 
.      .       2.60 
.      .       3.70 
.      .       1.26 
.      .     19.30 

Sulphuric  acid     . 
Sulphur                .      . 

1.84 
2.03 

Susrar 

1  59 

Tin            .... 

7.29 

Water,  at  0°  C.  .     . 
Water,  at  4°  C.  .      . 
Water,  sea 
Zinc 

.       0.999 
.       1.00 
1.03 
7.00 

Granite 

2.70 

Human  body 
Ice 

.      .       0.89 
092 

600. 

Boston,  Mass.    . 
Ithaca,  N.  Y.     . 
Chicago,  111. 
Cleveland  O 

VALUES 

.      .      .     980.38 
.      .      .     980.29 
.      .      .     980.26 
98023 

OF    G 

Washington,  D.  C. 
Cincinnati,  O.    . 
Charlottes  ville,  Va. 
Denver,  Col. 
Pike's  Peak,  Col.     . 

POINTS 

Aluminum 

.      .     980.10 
.      .     979.99 
.      .     979.92 
.      .     979.60 
.      .     978.94 

.      .       657° 

Philadelphia,  Pa. 
601. 
Mercury  . 

.      .      .     980.18 

MELTING 

.      .      .  -38.8° 

Phosphorus 

443 

Silver 

.      .       961 

Sulphur 

115 

Gold         .... 

.      .      1063 

Tin      .... 
Bismuth 

...       232 
260 

.      .     1084 

Iron 

.      .      1100 

Cadmium 

320 

Steel                      .      . 

.      .      1350 

Lead   .... 
Zinc 

...       327 
419 

Platinum              .      . 

1778 

Iridium 

2200 

394 


HIGH  SCHOOL  PHYSICS 


602. 


BOILING    POINTS 


Ethylene -  103° 

Ammonia —38.5 

Chlorine -33.6 

Ether 35 

Carbon  bisulphid       ...        46 
Chloroform  61 


Alcohol 78° 

Benzene 80 

Toluene 110 

Turpentine 160 

Glycerine 290 

Mercury 357 


BOILING  POINTS  OF  WATER  UNDER  DIFFERENT  PRESSURES 


73 

74 
75 


98.88' 
99.26 
99.63 


76 

77 
78 


100.00° 

100.37 

100.73 


604.        EXTREMELY  Low  FREEZING  AND  BOILING  POINTS 

Freezing  Point  Boiling  Point 

. . -     103° 

-  268.8 

-  252.5 

-     194 

. .  -     181 


Ethylene     

Helium    

Hydrogen- -  260° 

Nitrogen —  210 

Oxygen -  227 


605. 


SPECIFIC    HEATS 


Water 1.000 

Ice '  0.505 

Ether 0.547 

Alcohol 0.602 

Tin 0.055 

Gold    .......  0.032 

Platinum  .  0.032 


Aluminum 0.214 

Glass 0.200 

Iron     .......  0.116 

Copper 0.094 

Mercury 0.033 

Lead 0.031 

Zinc  0.094 


606.         NUMBER    OF    GRAMS    OF    WATER    VAPOR    REQUIRED    TO 
SATURATE    THE    AIR,    PER    CUBIC    METER 


-  10°  C. 


2.363  g. 

2.546 

2.741 

2.949 

3.171 

3.407 

3.659 

3.926 

4.211 

4.513 


0°  C 4.835  g. 


5.176 
5.538 
5.922 
6.330 
6.761 
7.219 
7.703 
8.215 
8.757 


10°  C. 

11 

12 

13 

14 

15 

16 

17 

18 

19 


9.330  g. 

9.935 
10.574 
11.249 
11.961 
12.712 
13.505 
14.339 
15.218 
16.144 


20< 
21 
22 
23 
24 


C. 


SUPPLEMENT 

17.118  g. 

25°  C  

22.796  g. 

30°  C. 

18.143 

26 

24.109 

31 

19.222 

27 

25.487 

32 

20.355 

28 

26.933 

33 

21.546 

29 

28.450 

34 

395 

30.039  g. 

31.704 

33.449 

35.275 

37.187 


607. 


HEATS    OF    COMBUSTION    IN    CALORIES    PER    GRAM 


Hydrogen 34700 

Gunpowder 700 

Dynamite 1300 

Sulphur 2200 

608.  HEATS    OF    COMBUSTION 

Bituminous  Coal 

Streator,  111 13,700 

Wilmington,  111.      .      .      .  14,000 

Saginaw,  Mich.        .      .      .  13,500 

Hocking  Valley,  O.       .      .  14,000 

Jackson,  0 14,000 

Turtle  Creek,  Pa.    .      .      .  15,000 

Youghiogheny,  Pa.       .      .  15,000 

Thacker,  W.  Va.      .      .      .  15,200 


Alcohol   . 
Illuminating  gas 
Wood      .      .      . 
Anthracite  coal 


.      .        7183 

.      .        6000 

about       4300 

8000 


IN    B.  T.  U.  PER    POUND 

Semi-Bituminous  Coal 

Blassburg,  Pa 13,500 

Pocahontas,  W.  Va.      .      .  15,700 

Cumberland,  Md.   .      .      .  16,300 

Anthracite  Coal 

Lackawanna      ....  13,900 

Lykens  Valley   ....  13,700 

Scranton       .      .      .      .      .  13,800 


609. 


INDICES    OF    REFRACTION 


Water 1.33 

Carbon  bisulphide      .      .      .  1.64 

Turpentine 1.47 

Alcohol  1.36 


Benzene 1.50 

Crown  glass     .     *.      .      .      .  1.52 

Flint  glass 1.62 

Diamond    ,  2.47 


610. 


CONVERSION    TABLES 


English  to 
1  mile 
1  mile              = 
1  foot 
1  inch              = 

Metric 
1.60935  km. 
1609.347  m. 
0.3048  m. 
2.54  cm. 

Metric  to  English 
1  kilometer    =      0.62137  mi. 
1  meter           =  0.0006214  mi. 
1  meter          =      3.28083  ft. 
1  centimeter  =        0.3937  in. 

1  cubic  foot    = 
1  gallon          = 

28.31701  1. 
3.78543  1. 

1  liter  =  0.03532  cu. 
1  liter  =  0.26417  gal. 

1  pound 
1  grain            = 

0.45359  kg. 
0.064800  g. 

1  kilogram  =  2.2046  Ib. 
1  gram  =  15.432  gr. 

396 


HIGH  SCHOOL  PHYSICS 


611. 


WIRE    GAUGE    VALUES,  AMERICAN    (B.  & 


Gauge 
no. 

Diam.  in 
mm. 

Diam.  in 
Mils 

Sq.  of  Diam. 
Mils 

Gauge 
no. 

Diam.  in 
mm. 

Diam.  in 
Mils 

Sq.  of  Diam. 
Mils 

0000 

11.684 

460.00 

211600.0 

19 

.899 

35.39 

1252.4 

000 

10.405 

409.64 

167805.0 

20 

.812 

31.96 

1021.5 

00 

9.266 

364.80 

133079.4 

21 

.723 

28.46 

810.1 

0 

8.254 

324.95 

105592.5 

22 

.644 

25.35 

642.7 

1 

7.348 

289.30 

83694.2 

23  • 

.573 

22.57 

509.5 

2 

6.544 

257.63 

66373.0 

24 

.511 

20.10 

404.0 

3 

5.827 

229.42 

52634.0 

25 

.455 

17.90 

320.4 

4 

5.189 

204.31 

41742.0 

26 

.405 

15.94 

254.0 

5 

4.621 

181.94 

33102.0 

27 

.361 

14.19 

201.5 

6 

4.115 

162.02 

26250.5 

28 

.321 

12.64 

159.8 

7 

3.665 

144.28 

20816.0 

29 

.286 

11.26 

126.7 

8 

3.264 

128.49 

16509.0 

30 

.255 

10.03 

100.5 

9 

2.907 

114.43 

13094.0 

31 

.227 

8.93 

79.7 

10 

2.588 

101.89 

10381.0 

32 

.202 

7.95 

63.2 

11 

2.305 

90.74 

8234.0 

33 

.180 

7.08 

50.1 

12 

2.053 

80.81 

6529.9 

34 

.160 

6.30 

39.7 

13 

1.828 

71.96 

5178.4 

35 

.143 

5.61 

31.5 

14 

1.628 

64.01 

4106.8 

36 

.127 

.  5.00 

25.0 

15 

1.450 

57.07 

3256.7 

37 

.113 

4.45 

19.8 

16 

1.291 

50.82 

2582.9 

38 

.101 

3.96 

15.7 

17 

1.150 

45.26 

2048.2 

39 

.090 

3.53 

12.5 

18 

1.024 

40.30 

1624.3 

40 

.080 

3.14 

9.9 

Sir  Isaac  Newton  (1642-1727), 
great  English  mathematician  and 
physicist.  Discovered  the  laws  of 
gravitation,  and  announced  laws 
of  motion. 


Galileo  (1566-1642),  Italian.  In- 
vestigated the  laws  of  falling  bodies 
by  dropping  weights  from  the  lean- 
ing tower  of  Pisa.  Invented  the 
telescope. 


Archimedes  (287-212  B.C.),  Syr- 
acuse, Sicily.  Discovered  the  laws 
of  the  lever,  and  the  principle  of 
buoyancy  known  as  the  Principle 
of  Archimedes. 


Lord  Kelvin  (Sir  William  Thomp- 
son), (1824-1907),  born  Belfast, 
Ireland.  Professor  of  physics,  Uni- 
versity of  Glasgow.  Great  mathe- 
matical physicist. 


James  Prescott  Joule  (1818- 
1889),  English  scientist.  Deter- 
mined the  mechanical  equivalent 
of  heat. 


James  Watt  (1736-1819),  Scotch 
instrument  maker.  Inventor  of 
the  modern  type  of  steam  en- 
gine. 


Alessandro  Volta  (1748-1827), 
Italian  physicist.  Early  investiga- 
tor of  current  electricity.  Voltaic 
cell  and  volt  were  named  in  his 
honor. 


Andre  Marie  Ampere  (1775- 
1836),  French  physicist.  Investi- 
gated magnetic  effects  of  currents. 
The  ampere,  unit  of  current 
strength,  given  his  name. 


Georg  Simon  Ohm  (1789-1854), 
German  scientist.  Announced  the 
electrical  law  named  in  his  honor 
(Ohm's  law). 


Michael  Faraday  (1791-1867), 
English  physicist  and  investigator 
in  electricity  and  magnetism. 
Called  the  "prince  of  experiment- 


ers/ 


Sir  William  Crookes,  English 
scientist,  born  1832.  Investigated 
the  nature  of  matter  in  highly 
exhausted  tubes,  now  known  as 
Crookes'  tubes. 


Wilhelm  Konrad  Roentgen,  Ger- 
man scientific  investigator,  born 
1845.  Discovered  X-rays,  also 
called  Roentgen  rays. 


James    Clerk-Maxwell     (1831-  Heinrich  Rudolph  Hertz  (1857- 

1879),  professor   of   physics,    Uni-  1894),  German  physicist.     Discov- 

versity    of    Cambridge,    England.  erer  of  electromagnetic  waves  pre- 

Announced  the  famous  electromag-  dieted  by  Maxwell's  theory, 
netic  theory  of  light. 


Hermann  von  Helmholtz  (1821-  Madame  Curie,  born  in  Warsaw, 
1894),  one  of  the  greatest  German  Poland,  1867.  Joint  discoverer 
physicists  and  mathematicians  of  with  her  husband,  Prof.  Curie  of 
his  day.  the  University  of  Paris,  of  the  ele- 

ment radium. 


SUPPLEMENT  397 


PROBLEMS 

MECHANICS 

1.  A  body  starting  from  rest  is  acted  upon  by  a  constant  force  which 
imparts  to  it  an  increase  in  velocity  of  5  ft.  per  second  each  second,     (a) 
Find  its  velocity  in  10  seconds,    (b)  How  far  will  it  travel  during  the  last  5 
seconds? 

2.  A  train  coming  into  a  station  has  at  a  given  instant  a  velocity  of 
10  ft.  per  second      Five  seconds  later  it  has  come  to  rest,     (a)  What  was 
the  negative  acceleration?     (b)  How  far  did  it  move  during  the  5  seconds? 

3.  A  body  falls  freely  a  distance  of  1000  ft.     Find  its  velocity  (a)  in 
feet;  (b)  meters. 

4.  A  car  starts  from  rest  and  in  10  seconds  its  velocity  is  20  ft.  per 
second.     Find  (a)  its  acceleration;    (b)  the  distance  it  travels  during  the 
10  seconds. 

5.  A  body  is  thrown  vertically  downward  from  a  cliff  800  ft.  in  height, 
with  a  velocity  of  10  ft.  per  second.     In  what  time  will  it  reach  the 
ground? 

6.  An  electric  car  is  running  at  the  rate  of  30  miles  per  hour.     The 
brakes  are  applied  and  the  car  is  stopped -in  30  seconds.     Find  (a)  the 
negative  acceleration;    (b)  the  distance  the  car  moved  after  the  brakes 
were  applied. 

7.  How  long  will  it  take  a  force  of  10  dynes  acting  on  a  mass  of  100 
grams  to  change  its  velocity  from  5  to  25  cm.  per  second? 

8.  A  stone  thrown  into  the  air  reaches  the  ground  in  5  seconds.     Find 

(a)  the  height  to  which  it  ascended;   (b)  the  velocity  with  which  it  struck 
the  ground. 

9.  A  ball  having  accelerated  motion  moves  10  ft.  the  first  second  and 
15  ft.  the  second.     Find  (a)  its  velocity  at  the  end  of  the  third  second; 

(b)  the  space  it  passes  over  during  the  third  second. 

10.  A  body  is  dropped  from  the  top  of  a  tower  300  ft.  in  height.     At  the 
same  instant  another  body  is  projected  vertically  upward  with  a  velocity 
of  300  ft.  per  second.     Find  at  what  point  above  the  ground  the  two 
will  pass  each  other. 

11.  A  flag  is  hoisted  to  the  masthead  of  a  vessel  a  distance  of  50  ft., 
during  which  time  the  vessel  moves  forward  100  ft.     Find  the  magnitude 
and  direction  of  the  actual  velocity  of  the  flag. 


398  HIGH  SCHOOL  PHYSICS 

12.  A  man  riding  on  an  electric  car,  which  is  running  at  the  rate  of  10 
miles  per  hour,  throws  off  a  package  at  right  angles  to  the  track  with  a 
velocity  of  10  ft.  per  second.  Find  the  magnitude  and  direction  of  the 
velocity  of  the  package. 

13.  Resolve  a  force  of  100  Ibs.  into  two  components  acting  at  an  angle 
of  60°  with  each  other. 

14.  The  wind  is  blowing  northeast  with  a  velocity  of  20  miles  per  hour. 
Resolve  this  velocity  into  two  components,  one  to  the  northward  and  one 
to  the  eastward. 

16.  A  weight  of  100  Ibs.  is  supported  by  two  ropes  fastened  to  a  beam, 
each  rope  making  an  angle  of  30°  with  the  beam.  Find  the  force  exerted 
on  each  rope. 

16.  Find  the  length  of  a  pendulum  that  makes  90  vibrations  per  min- 
ute, giving  the  result  in  (a)  meters;   (b)  feet. 

17.  A  weight  attached  to  a  string  is  suspended  from  an  upper  story  of 
a  building.     The  weight  swinging  as  a  pendulum  just  clears  the  ground. 
It  makes  10  vibrations  per  minute.     Find  the  length  of  the  string. 

18.  An  ounce  bullet  is  shot  from  a  9  Ib.  gun  with  a  velocity  of  1000  ft. 
per  second.     Find  the  velocity  of  the  gun's  recoil. 

19.  A  boy  throws  a  stone  weighing  8  oz.  with  a  velocity  of  20  ft.  per 
second.     Compare  the  momentum  of  the  stone  with  that  of  a  freight  car 
weighing  20  tons  and  moving  with  a  velocity  of  8  miles  per  hour. 

20.  A  body  having  a  mass  of  20  grams  moves  with  a  velocity  of  2  meters 
per  second.     Find  its  kinetic  energy  in  (a)  kilogram  meters;    (b)  gram 
centimeters;  (c)  ergs. 

21.  A  100  ton  engine  is  moving  with  a  velocity  of  20  miles  per  hour. 
Find  its  kinetic  energy  in  foot  pounds. 

22.  A  body  having  a  mass  of  10  Ibs.  falls  vertically  for  10  seconds. 
Find  its  kinetic  energy  in  (a)  foot  poundals;  (b)  foot  pounds. 

23.  A  force  of  10  Ibs.  acts  for  10  seconds  on  a  mass  of  10  Ibs.     Find  (a) 
the  velocity  at  the  end  of  the  10  seconds;   (b)  the  energy  in  foot  pounds. 

24.  A  mass  of  2  Ibs.  is  attached  to  the  rim  of  a  wheel  having  a  radius 
of  2  ft.     The  wheel  rotates  at  the  rate  of  120  times  a  minute.     Find  the 
centrifugal  force  exerted  by  the  body. 

25.  Find  the  horse  power  of  an  engine  that  can  raise  10  tons  to  a  height 
of  10  feet  in  10  minutes. 

26.  A  windmill  pumps  5  tons  of  water  from  a  well  50  ft.  deep  in  10 
minutes.     Find  its  horse  power. 

27.  It  is  estimated  that  700  tons  of  water  passes  over  Niagara  Falls 
per  minute.     The  distance  which  it  falls  is  160  ft.     Compute  the  horse 
power  of  Niagara  Falls. 

28.  The  wind  drives  a  boat  at  the  rate  of  10  miles  an  hour  against  an 


SUPPLEMENT  399 

average  resistance  of  500  Ibs.     Compute  the  horse  power  furnished  by  the 
wind. 

29.  A  force  of  50  Ibs.  is  applied  to  one  end  of  a  10  ft.  lever  of  the  second 
class.     A  weight  to  be  lifted  is  placed  2  ft.  from  the  other  end  of  the  lever. 
What  resistance  will  the  force  overcome? 

30.  A  uniform  bar  10  ft.  in  length  and  weighing  2  Ibs.  to  the  foot  is 
used  as  a  lever  of  the  first  class.     The  fulcrum  is  placed  2  ft.  from  the  end. 
Taking  into  account  the  weight  of  the  lever,  what  force  will  be  required 
at  one  end  to  overcome  a  resistance  of  800  Ibs.  at  the  other? 

31.  A  given  bicycle  wheel  is  28  inches  in  diameter.     The  driving 
sprocket  is  8  inches  in  diameter,   the  small  sprocket  2  inches.     How 
many  times  will  the  rider  have  to  move  his  feet  up  and  down  in  going 
a  mile? 

32.  The  axle  of  a  windlass  is  4  inches  in  diameter;  the  crank  by  which 
the  windlass  is  turned  is  x  inches.     A  force  of  10  Ibs.  applied  to  the  end  of 
the  crank  supports  100  Ibs.  on  the  rope  passing  around  the  axle.     Find  the 
value  of  x. 

33.  The  pilot  wheel  on  a  boat  is  4  ft.  in  diameter;  the  axle  6  inches  in 
diameter.     What  force  must  the  pilot  apply  to  the  wheel  in  order  to  steer 
the  boat,  assuming  that  the  steering  resistance  against  the  motion  of  the 
wheel  is  300  Ibs.? 

34.  A  weight  of  2  tons  is  to  be  raised  by  a  jackscrew,  the  lever  of  which 
is  3  ft.  long.     What  force  must  be  applied,  assuming  that  the  screw  threads 
are  2  to  the  inch? 

35.  Show  by  diagram  how  you  would  arrange  3  pulleys  so  as  to  lift 
the  greatest  weight. 

36.  The  diameter  of  a  wheel  of  a  copying  press  is  14  inches.     On  the 
screw  there  are  5  threads  to  the  inch.     If  the  wheel  be  turned  with  a  force 
of  20  Ibs.  applied  to  its  outer  rim,  what  will  be  the  downward  thrust  exerted 
by  the  screw? 

37.  A  cubical  tank  4  ft.  wide,  6  ft.  deep,  and  10  ft.  long  is  filled  with 
water.     Find  (a)  the  force  exerted  on  the  bottom;  (b)  on  one  end. 

38.  Over  the  top  of  the  tank  of  problem  37  there  is  fitted  a  tight  cover, 
into  the  surface  of  which  there  is  inserted  a  plug  having  a  cross  sectional 
area  of  10  sq.  in.     A  force  of  10  Ibs.  is  applied  to  the  plug.     Find  the  force 
transmitted  to  one  side  of  the  tank  due  to  the  force  on  the  plug. 

39.  A  hydraulic  elevator  is  operated  by  water  from  the  city  mains 
under  a  pressure  of  70  Ibs.  per  sq.  in.     The  cross  sectional  area  of  the  piston 
is  70  sq.  in.     What  load  can  be  lifted  due  to  the  water  pressure? 

40.  The  diameter  of  the  small  piston  of  a  hydraulic  press  is  2  inches; 
that  of  the  large  piston,  2  ft.     A  weight  of  100  Ibs.  applied  to  the  small 
piston  will  exert  what  upward  force  on  the  large  piston? 


400  HIGH  SCHOOL  PHYSICS 

41.  The  weight  of  a  piece  of  lead  is  1  kg.;   the  density  of  lead  is  11.3. 
Find  the  volume  of  the  piece  of  lead. 

42.  The  100-gram  weight  of  a  set  of  weights  is  made  of  brass,  the  density 
of  which  is  8.4.     Find  the  volume  in  cc.  of  the  100-gram  weight. 

43.  Determine,  by  reference  to  the  density  tables,  the  volume  of  a 
vessel  which  holds  1  kg.  of  ether. 

44.  The  dimensions  of  a  brick  are  8x4x2  inches;   its  weight  4  Ibs. 
Find  its  density. 

46.  If  you  were  offered  a  cubic  foot  of  gold  provided  you  could  carry 
it,  with  the  understanding  that  you  were  to  forfeit  $10  in  case  you  could 
not  lift  it,  would  you  accept  the  offer? 

46.  An  ice  box  is  3x2x1  ft.     When  it  is  filled  with  ice,  about  how 
many  pounds  does  it  hold,  assuming  that  the  density  of  ice  is  0.9? 

47.  Compute  the  mass  of  the  earth  in  tons,  assuming  its  radius  to  be 
4000  miles  and  its  average  density  5.5. 

48.  The  difference  between  the  barometric  reading  at  the  bottom  and 
the  top  of  the  IJiffel  Tower,  Paris,  which  is  1000  ft.  in  height,  is  1.1  inch. 
Compute  the  normal  barometric  reading  at  Denver,  which  is  5400  ft.  above 
sea  level. 

49.  As  a  balloon  rises  will  the  fall  of  the  barometer  be  proportional  to 
the  distance  passed  over?     Why? 

50.  Over  what  height  may  water  be  siphoned  on  a  mountain  1  mile 
above  sea  level,  assuming  that  an  ascent  of  90  ft.  is  equivalent  to  a  fall  in 
the  barometric  column  of  0.1  inch.? 

51.  Consult  the  density  tables  and  compute  the  approximate  weight 
of  the  air  in  a  room  10  x  20  x  30  ft. 

52.  Into  what  space  must  30  cu.  ft.  of  air  be  compressed  in  order  that 
its  density  be  increased  threefold? 


HEAT 

53.  Reduce  -  10°,  +  10°,  +  41°,  +  68°,  +  180°  F.  to  the  C.  scale. 

54.  Mercury  boils  at  +  357°  C.     Finds  its  boiling  point  on  the  F.  scale. 

55.  Ordinary  room  temperature  is  70°  F.     What  is  this  on  the  C.  scale? 

56.  How  much  must  an  iron  rod  40  ft.  long  be  heated  to  expand  1  inch, 
the  coefficient  of  linear  expansion  of  iron  being  0.000012? 

57.  The  temperature  of  liquid  air  is  —  181°  C.     Express  this  tem- 
perature on  the  F.  scale. 

58.  How  much  will  an  iron  telegraph  wire  1000  ft.  in  length  contract 
if  the  temperature  falls  20°  C.? 

69.   How  many  grams  of  boiling  water  at  100°  C.  must  be  added  to  5 


SUPPLEMENT  401 

liters  of  cold  water  at  5°  C.  in  order  that  the  resulting  temperature  be 
25°  C? 

60.  How  much  mercury  at  100°  C.  must  be  added  to  100  grams  of  water 
at  10°  C.  in  order  that  the  resulting  temperature  of  the  mixture  be  20°  C.? 

61.  One  kilogram  of  ice  is  melted  and  the  temperature  of  the  water  is 
raised  to  the  boiling  point.     How  many  calories  of  heat  are  required? 

62.  Ten  pounds  of  ice  are  melted  and  the  temperature  of  the  water 
raised  to  the  boiling  point.     Find  the  number  of  B.T.U.  required. 

63.  A  copper  vessel  having  a  mass  of  100  grams  contains  300  grams  of 
water  at  100°  C.     How  many  grams  of  ice  at  0°  C.  must  be  put  into  the 
water  in  order  to  lower  the  temperature  to  50°  C.? 

64.  One  hundred  grams  of  steam  at  100°  C.  are  changed  to  ice  at  0°  C. 
How  many  calories  of  heat  are  given  out? 

65.  One  hundred  grams  of  ice  at  —  10°  C.  are  changed  to  steam  at 
100°  C.     How  many  calories  of  heat  are  required,  assuming  the  specific 
heat  of  ice  to  be  0.5? 

66.  A  certain  mass  of  gas  at  20°  C.  has  a  volume  of  1  liter.     Find  its 
volume  at  — 10°  C.,  the  pressure  remaining  constant. 


ELECTRICITY  AND  MAGNETISM 

67.  A  wire  10  ft.  long  has  a  diameter  of  1  mm.     What  must  be  the 
diameter  of  a  second  wire  20  ft.  long  in  order  to  offer  half  the  resistance  of 
the  first? 

68.  If  the  resistance  of  a  given  wire  10  m.  long  and  2  mm.  in  diam- 
eter be  10  ohms,  what  length  of  wire  of  the  same  material  1  mm.  in  diameter 
will  be  required  to  give  a  resistance  of  5  ohms? 

69.  The  diameter  of  a  copper  wire  10  ft.  in  length  is  0.025  inches.    Find 
by  reference  to  Table  of  Constants  (a)  its  diameter  in  mils;  (b)  its  resist- 
ance in  ohms. 

70.  Three  wires  whose  resistances  are  5,  6,  and  7  ohms  respectively  are 
joined  in  parallel.     Find  the  resistance  of  the  three  wires  thus  connected. 

71.  What  E.M.F.  is  necessary  to  maintain  a  current  of  0.5  ampere 
through  a  resistance  of  70  ohms? 

72.  A  battery  of  5  cells  is  connected  in  series  with  an  external  resistance 
of  50  ohms.     The  E.M.F.  of  each  cell  is  1.5  volts  and  its  internal  resist- 
ance 1  ohm.     What  current  does  the  battery  furnish? 

73.  The  E.M.F.  of  a  battery  is  10  volts  and  the  strength  of  current 
which  it  maintains  through  a  resistance  of  10  ohms  is  0.5  ampere.     Find 
the  internal  resistance  of  the  battery. 

74.  An  electromagnet  of  10  ohms  resistance  and  a  rheostat  of  20  ohms 


402  HIGH  SCHOOL  PHYSICS 

resistance  are  connected  in  series.    A  current  of  0.5  amperes  flows  through 
the  circuit.     Find  the  fall  of  potential  over  each  instrument. 

75.  A  difference  of  potential  of  10  volts  is  applied  to  the  terminals  of  a 
telegraph  relay,  giving  rise  to  a  current  of  0.1  ampere.     Find  the  resistance 
of  the  relay. 

76.  An  arc  lamp  under  a  pressure  of  50  volts  runs  on  a  current  of  5 
amperes.     Find  (a)  the  power  expended  in  kilowatts;    (b)  the  cost  of 
running  this  lamp  for  5  hours  at  10  cents  per  kilowatt  hour. 

77.  A  conductor  having  a  resistance  of  10  ohms  carries  a  current  of 
5  amperes.     How  much  energy  is  consumed  in  10  minutes  in  (a)  calories? 
(b)  ergs? 

78.  How  much  heat  is  developed  per  hour  by  a  55  watt  incandescent 
lamp  on  a  110  volt  circuit? 

79.  A  current  of  5  amperes  at  a  pressure  of  110  volts  passes  through 
the  primary  of  an  induction  coil,  having  200  turns  of  wire  in  the  primary 
and  2000  in  the  secondary.     What  will  be  the  strength  of  the  induced 
current  in  the  secondary,  assuming  that  there  are  no  losses? 

80.  An  induction  coil  has  200  turns  in  its  primary  and  60,000  in  its 
secondary.     A  pressure  of  10  volts  is  applied  to  the  primary.     What 
voltage  will  be  induced  in  the  secondary? 

81.  A  transformer  is  used  to  step  an  alternating  current  having  a  pres- 
sure of  1000  volts  down  to  one  of  50  volts.     If  there  are  500  turns  of  wire 
in  the  primary,  how  many  will  there  be  in  the  secondary? 


SOUND 

82.  A  bullet  fired  with  a  velocity  of  1200  ft.  per  second  is  heard  to 
strike  a  target  5  seconds  after  leaving  the  rifle.     Find  the  distance  of  the 
target,  the  temperature  being  20°  C. 

83.  The  Eiffel  Tower  is  1000  ft.  high.     A  bell  is  struck  at  the  top.     In 
what  time  will  the  sound  reach  a  point  1000  ft.  from  the  center  of  the  base, 
the  temperature  being  68°  F.? 

84.  A  given  tuning  fork  makes  300  vibrations  per  second.     What  effect 
will  a  rise  of  20°  C.  have  upon  the  wave  length  produced  by  this  fork? 

85.  On  a  day  when  the  temperature  is  77°  F.  a  report  of  a  rifle  is  heard 
5  seconds  after  the  puff  of  smoke  is  seen.     How  far  away  is  the  rifle? 

86.  A  wave  length  of  the  sound  wave  given  out  by  an  organ  pipe  is 
5  meters  when  the  temperature  is  20°  C.     Find  the  vibration  number  of 
the  pipe. 

87.  Two  strings  on  a  piano  give  3  beats  per  second.     If  the  vibration 
number  of  one  of  the  strings  is  320,  what  is  that  of  the  other? 


SUPPLEMENT  403 

88.  A  closed  organ  pipe  produces  waves  6  ft.  in  length,     (a)  What  is 
the  length  of  the  pipe?     (b)  What  is  the  length  of  an  open  pipe  that  will 
produce  waves  of  the  same  length? 

89.  A  given  string  stretched  by  a  force  of  16  Ibs.  makes  256  vibrations 
per  second.     What  will  be  the  vibration  rate  if  the  stretching  force  be 
increased  to  25  Ibs.? 

90.  A  string  1  meter  long  makes  512  vibrations  per  second.     What  will 
be  the  frequency  of  the  string  if  its  length  be  decreased  by  25  cm.? 

LIGHT 

91.  The  page  of  a  book  is  held  1  ft.  from  a  given  light.     It  is  then 
removed  to  a  distance  of  5  ft.     Compare  the  intensities  of  light  on  the 
page  in  the  two  cases. 

92.  A  gas  flame  placed  6  ft.  from  the  screen  of  a  Bunsen  photometer 
illuminates  it  as  much  as  a  standard  candle  placed  at  a  distance  of  6  inches. 
What  is  the  candle  power  of  the  gas  flame? 

93.  It  is  estimated  that  the  nearest  fixed  star  is  25,000,000,000,000 
miles  from  the  earth.     Find  the  time  required  for  light  to  travel  from  this 
star  to  the  earth. 

94.  Two  planes  are  placed  at  a  distance  of  2  ft.  and  3  ft.  respectively 
from  a  given  source  of  light.     What  must  be  the  relative  area  of  the  two 
planes  in  order  that  they  intercept  the  same  amount  of  light? 

95.  The  radius  of  curvature  of  a  concave  mirror  is  30  cm.     An  object 
is  placed  at  a  distance  of  50  cm.  from  the  vertex  of  the  mirror,     (a)  Find 
the  distance  of  the  image  from  the  mirror,     (b)  Will  it  be  real  or  virtual? 

96.  A  candle  placed  20  cm.  from  the  vertex  of  a  concave  mirror  gives 
a  real  image  50  cm.  from  the  mirror.   Find  (a)  the  focal  length  of  the  mirror; 
(b)  its  radius  of  curvature. 

97.  Light  travels  in  a  given  liquid  with  a  velocity  of  136,000  miles  per 
second.     Find  the  index  of  refraction  of  this  liquid. 

98.  An  object  is  placed  70  inches  in  front  of  a  convex  lens,  the  focal 
length  of  which  is  4  inches,     (a)  Find  the  distance  of  the  image  from  the 
lens,     (b)  What  will  be  its  size  as  compared  with  that  of  the  object? 

99.  A  convex  lens,  the  focal  length  of  which  is  2  ft.,  is  placed  14  ft. 
from  a  screen,     (a)  Where  must  a  candle  be  placed  in  order  that  its  image 
be  focused  upon  the  screen?     (b)  What  will  be  the  size  of  the  image  as 
compared  with  that  of  the  candle? 

100.  A  convex  lens  having  a  focal  length  of  3  cm.  is  held  2.7  cm.  from 
an  object,     (a)  How  far  will  the  image  be  from  the  lens?     (b)  Will  it  be 
real  or  virtual? 


INDEX 


Aberration,  chromatic,  353;  spher- 
ical, 326,  336 

Absolute,  temperature,  138;  unit 
of  force,  27;  zero,  138 

Absorption,  of  gases,  120;  of  radi- 
ant energy,  164 

Acceleration,  17;  value  due  to 
gravity,  21 

Achromatic  lens,  354 

Action  of  points,  193 

Adhesion,  106 

Aeroplane,  371 

Agonic  line,  181 

Air,  compressibility  of,  88;  pres- 
sure of,  91;  air  brake,  air  pump, 
99;  air  ship,  370;  air  thermom- 
eter, 128 

Alternating  current,  247 

Amalgamation  of  zinc,  200 

Ammeter,  220 

Ampere,  212 

Amplitude  of  vibration,  45 

Analysis  of  light,  353 

Angle,  of  deviation,  328;  reflec- 
tion, 319;  refraction,  328;  inci- 
dence, 319 

Anode,  206 

Antinode,  297 

Arc  light,  235 

Archimedes'  principle,  79 

Armature,  247 

Artesian  well,  77 

Astigmatism,  344 

Astronomical  telescope,  387 

Atmospheric  pressure,  88;   91 

Atom,  4 

Attraction,  electrical,  184 

Audibility,  limits  of,  305 

Avoirdupois  pound,  12 


Balance,  12 

Balloon,  103 

Bar  magnet,  174 

Barometer,  92 

Battery,  198;     lead    storage,    211; 

Edison  storage,  211 
Beam  of  light,  311 
Beats,  290 
Bell,  electric,  256 
Boiling,  141-143;   laws  of,  143 
Boyle's  law,  94 
Bright  line  spectrum,  351 
British  thermal  units,  130 
Brushes,  electrical,  247 
Bunsen  photometer,  317 
Buoyancy,  of  water,  79;  of  air,  102 

Calorie,  129 

Camera,  315,  346 

Capillarity,  116;    laws  of,  118 

Car,  electric,  255 

Cathode,  206;  ray,  264 

Caustic,  326 

Cells,  kinds  of,  203;  in  series,  229; 
in  parallel,  230 

Center,  of  buoyancy,  81;  of  grav- 
ity, 4;  of  oscillation,  50;  of  per- 
cussion, 51 

Centigrade  thermometer,  126 

C.G.S.  system,  14 

Centrifugal  force,  36 

Centripetal  force,  36 

Charles,  law  of,  138 

Chemical  change,  5 

Chord,  major,  293;    minor,  293 

Chromatic  aberration,  353 

Circuit,  electrical,  198 

Clinical  thermometer,  129 

Coefficient  of  elasticity,  110 


406 


INDEX 


Coefficient  of  expansion,  133 

Cohesion,  106 

Cold,  150-152 

Color,  348 

Communicating  tubes,  76 

Commutator,  247 

Compound  bar,  134 

Concave  lens,  335 

Condensation  of  wave,  276 

Condenser,  electrical,  190,  261 

Condensing  pump,  99 

Conduction  of  heat,  153 

Conductors,  in  series,  223;  paral- 
lel, 223 

Conservation  of  energy,  57 

Continuous  spectrum,  351 

Convection,  156 

Convex  lens,  335 

Corpuscles,  4 

Coulomb,  213 

Critical  angle,  332 

Crookes'  tube,  263 

Crystallization,  113 

Current,  effect  of,  heating,  231; 
magnetic,  213 

Current  electricity,  197 


Daniell  cell,  203 

D'Arsonval  galvanometer,  218 

Day,  solar,  12 

Declination,  181 

Density,  82 

Dew  point,  148 

Dewar  flask,  156 

Dialysis,  122 

Diatonic  scale,  294 

Diffusion,  119,  327 

Dipping  needle,  180 

Dispersion,  349 

Dissociation  theory,  205 

Distillation,  149 

Dry  cell,  204 

Ductility,  112 

Dynamo,  245;    A.C.,    247;     D.C., 

248 
Dyne,  27 


Ear,  304 

Earth  a  magnet,  180 

Echo,  281 

Efficiency,  58 

Elasticity,  108 

Electric  arc,  235;  bell,  256;  cur- 
rent, 191,  197;  flatiron,  231; 
generator,  246;  motor,  251; 
power,  237;  soldering  iron,  231; 
telegraph,  256;  waves,  268 

Electrode,  197 

Electrolysis,  206 

Electrolyte,  197 

Electrolytic  cell,  206 

Electromagnet  217 

Electromotive  force,  199 

Electron  theory,  4 

Electrophorus,  188 

Electroplating,  209 

Electroscope,  186 

Electrotyping,  209 

Energy,  55;  conservation  of,  57; 
kinetic,  55;  potential,  55 

Engine,  steam,  167 

Erg,  53 

Ether,  310 

Equilibrium,  43 

Evaporation,  114 

Expansion,  132 

Extension,  3 

Eye,  342 

Fahrenheit  thermometer,  126 

Falling  bodies,  20 

Far  sight,  344 

Fireless  cooker,  355 

Flats  and  sharps,  295 

Fluids,  70;  pressure  in,  73 

Fluoroscope,  267 

Focal  length,  of  lens,  of  mirror,  319 

Focus,  of  lens,  334;   of  mirror,  319 

Foot  pound,  53 

F.P.S.  System,  14 

Force,  15;   composition  of,  28;  how 

measured,  26;    moment   of,  61; 

resolution  of,  32;    units  of,  26 
Force  pump,  99 


INDEX 


407 


Fraunhofer  lines,  351 

Friction,  57 

Fundamental,  tone,  297;    units,  7 

Fuse  plug,  237 

Fusion,  139;   heat  of,  140 

Galvanometer,  218 

Gas  engine,  168 

Gases,  88 

Gay-Lussac's  law,  138 

Geissler  tube,  263 

Grain,  12 

Gram,  12 

Gravitation,  38;  law  of,  39 

Gravitational  unit  of  force,  27 

Gravity,  6,  39;  acceleration  of,  17; 

cell,  203;   center  of,  40;  specific, 

83 

Heat,  123;  conduction  of,  153; 
convection  of,  158;  due  to  elec- 
tric current,  231;  mechanical 
equivalent  of,  166;  of  fusion, 
10;  of  vaporization,  145;  spe- 
cific, 130;  transmission  of,  152 

Hooke's  law,  109 

Horse  power,  54 

Humidity,  146 

Hydraulic,  elevator,  367;  press,  72 

Hydrometer,  87 

Hydrostatic  paradox,  75 

Ice  machine,  152 

Illumination,  316 

Image,  319;  by  lens,  337;  by 
mirrors,  320;  through  small 
apertures,  314 

Incandescent  lamp,  232 

Inclined  plane,  65 

Index  of  refraction,  332 

Induction,  charging  by,  185;  elec- 
trostatic, 183;  magnetic,  175; 
self-induction,  244 

Induction  coil,  259 

Inertia,  22 

Intensity,  of  illumination,  316;  of 
sound,  2&2 


Interference,  of  light,  357;  of  sound, 

289 

Interval,  musical,  293 
Ion,  205 

Jack  screw,  67 

Joule,  53 

Joule's  experiment,  165 

Key  note,  294 
Kilogram,  12 
Kilogram  meter,  53 
Kilowatt,  54 
Kilowatt  meter,  238 

Lactometer,  88 

Lamp,  arc,  235;  incandescent,  232 

Lantern,  projection,  388 

Law,  3;  Boyle's,  94;  Lenz's, 
245;  Ohm's,  221;  Charles',  138; 
of  gravitation,  39;  of  inverse 
squares,  316;  of  machines,  59; 
Pascal's,  71;  reflection,  318; 
refraction,  331 

Laws,  of  falling  bodies,  20;  of 
motion,  22;  of  air  columns,  300; 
of  strings,  298;  of  the  pendulum, 
48;  of  centrifugal  force,  36;  of  par- 
allel currents,  217;  of  magnetic 
attraction  and  repulsion,  174; 
of  electrostatic  attraction  and 
repulsion,  184 

Leclanche  cell,  204 

Length,  unit  of,  11 

Lens,  334;    achromatic,  354 

Lenz's  law,  244 

Levers,  61 

Ley  den  jar,  189 

Lift  pump,  97 

Light,  309;  analysis,  353;  prop- 
agation, 310;  reflection,  318; 
refraction,  328;  velocity,  313; 
synthesis,  353 

Lightning,  193;  rod,  195 

Line  of  direction,  42         ' 

Liquids,  73 

Liter,  H 


408 


INDEX 


Local  action,  200 
Lode  stone,  172 
Longitudinal  vibration,  276 
Loudness  of  sound,  282 

Machines,  57;  law  of,  59 

Magdeburg  hemispheres, 

Magnetic,  field,  175;  lines  of  in- 
duction, 175;  substance,  172; 
transparency,  177 

Magnets,  172 

Major  chord,  293 

Malleability,  113 

Mass,  7;  units  of,  12 

Matter,  1;  properties  of,  3;  states 
of,  5 

Mechanical  advantage,  60 

Mechanical  equivalent  of  heat,  166 

Mechanics,  15 

Melting  point,  139 

Mercury  air  pump,  101 

Metacenter,  82 

Meter,  11 

Metric  units,  7-12 

Microscope,  compound,  387;  simple, 
341 

Minor  chord,  293 

Mirrors,  319 

Molecular  forces,  106 

Molecules,  4 

Moment  of  a  force,  61 

Momentum,  23 

Morse  alphabet,  258 

Motion,  15-17;    laws  of,  22 

Motor,  electric,  251 

Multiple  reflection,  319 

Musical,  notes,  293;  scales,  294; 
sounds,  292 


Near  sight,  343 

Newton's  law  of   gravitation, 

laws  of  motion,  22 
Node,  297 
Noise,  292 

Octave,  293 
Ohm,  213 


39; 


Ohm's  law,  223 
Opaque  bodies,  309 
Optical  center,  335 
Organ  pipe,  300 
Oscillation,  center  of,  50 
Osmotic  pressure,  121 
Overtone,  297 

Pascal's  law,  71 

Pencil  of  light,  311 

Pendulum,  44;  simple,  46;  com- 
pound, 46;  laws  of,  48 

Penumbra,  313 

Percussion,  center  of,  50 

Period  of  vibration,  45 

Phenomenon,  2 

Photometer,  317 

Physical  change,  5 

Physics,  1 

Pipes,  299 

Pitch,  291 

Plumb  line,  41 

Polarization,  201 

Poles  of  a  magnet,  172 

Potential,  electrical,  191,  199 

Pound,  12 

Power,  53;  units  of,  54 

Pressure,  70;  of  fluids,  73;  gases,  88 

Primary  bow,  350 

Principal,  axis,  320,  335;  focus,  321, 
335 

Principle  of  Archimedes,  79 

Proof  plane,  187 

Pulleys,  63 

Pump,  air,  99;  compression,  100; 
force,  99;  lift,  97 

Quality  of  sound,  296 

Radiation,  162 
Radioactivity,  390 
Radiograph,  266 
Rainbow,  350 
Rarefaction,  276 
Ray  of  light,  311 
Reflection,  318 
Refraction,  328 


INDEX 


409 


Relay,  382 
Resistance  box,  221 
Resistance,  laws  of,  221 
Resolution  of  forces,  32 
Resonance,  284 
Resultant,  31 
Roentgen  rays,  265 

Saccharimeter,  88 

Screw,  66 

Second,  12 

Segmental  vibration,  297 

Self-induction,  244 

Shadows,  312 

Sharps  and  flats,  295 

Sight,  311 

Singing  flame,  290 

Siphon,  96 

Siren,  291 

Solenoid,  216 

Sonometer,  298 

Sound,  273 

Sounder,  telegraph,  258 

Specific  gravity,  83 

Specific  heat,  130 

Spectroscope,  352 

Spectrum,  348 

Spherical  aberration,  326,  336 

Spherical  mirror,  320 

Stability,  43 

Starting  box,  253 

Steam  engine,  167 

Storage  battery,  210 

Strings,  laws  of,  298 

Surface  tension,  115 

Sympathetic  vibrations,  284 

Synthesis  of  light,  353 

Tables,  393 

Tangent  galvanometer,  218 

Telegraph,  256;  key,  258;  sounder, 

258;    relay,  382;    wireless,  268 
Telephone,  259 
Telescope,  387 

Temperature,  124;    absolute,  138 
Tempered  scale,  296 
Tenacity,  107 


Theory,  2 

Thermometer,  125;  limitations  of, 
128;  Centigrade,  126;  Fahren- 
heit, 126;  clinical,  129;  air,  128 

Thermos  bottle,  156 

Thunder,  195 

Time,  12 

Tone,  fundamental,  297;  over- 
tone, 297 

Torricelli's  experiment,  90 

Transformer,  253 

Translucent,  309 

Transmission  of  heat,  152 

Transparent  bodies,  309 

Transverse  waves,  276 

Tungsten  lamp,  234 

Tuning  fork,  293 

Turbine,  engine,  375;    wheel,  366 

Units,  heat,  129;  length,  11;  mass, 

12;  time,  12 
Umbra,  313 
Unison,  293 

Vacuum,  100 
Vapor  pressure,  145 
Vaporization,  143;  heat  of,  145 
Velocity,    16;  of    sound,    279;     of 

light,  313 

Ventilation,  157-162 
Vibration,  amplitude  of,  45;  simple, 

45;  complete,  45;  period  of,  45 
Viscosity,  116 
Visual  angle,  344 
Vocal  organs,  302 
Voice,  range  of,  303 
Volt  meter,  220 
Voltaic  cell,  197 
Volume,  unit  of,  11 

Water,  electrolysis  of,  206;   wheels, 

78;   jet  pump,  101 
Watt,  54 

Watt-hour  meter,  238 
Waves,     274;    longitudinal,      276; 

transverse,    276;  length  of,    277; 

sound   waves,  276;   light   waves, 


410  INDEX 

310;  water  waves,  275;    electric,      Wireless  telegraph,  268 

268  Work,  52;    units  of,  52 

Wedge,  66 

Weight,  6,  39,   40;   law  of,  39;   of      X-rays,  265 
air,  89 

Wheatstone  bridge,  227  Yard,  10 

Wheel  and  axle,  63 

Windlass,  63  Zero,  absolute,  138 


14  DAY  USE 

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